Show transcribed image text. Named after Alexandru T. Balaban Vertices 112 Edges 168 Radius 6 Diameter 8 Girth 11 Automorphisms 64 Chromatic number 3 Chromatic index 3 Properties Cubic Cage Hamiltonian In the mathematical field of graph theory, the Balaban 11-cage or Balaban (3-11)-cage is a 3-regular graph with 112 vertices and 168 edges named after Alexandru T. Balaban. Answer to Draw the following: a. K3 b. a 2-regular simple graph c. simple graph with = 5 & = 3 d. simple disconnected graph with 6 vertices e. graph that is This page is modeled after the handy wikipedia page Table of simple cubic graphs of “small” connected 3-regular graphs, where by small I mean at most 11 vertices.. Yes. Graphs; Discrete Math: In a simple graph, every pair of vertices can belong to at most one edge and from this, we can estimate the maximum number of edges for a simple graph with {eq}n {/eq} vertices. Draw two such graphs or explain why not. There is (up to isomorphism) exactly one 4-regular connected graphs on 5 vertices. Must Do Coding Questions for Companies like Amazon, Microsoft, Adobe, ... Top 40 Python Interview Questions & Answers, Top 5 IDEs for C++ That You Should Try Once. What if the degrees of the vertices in the two graphs are the same (so both graphs have vertices with degrees 1, 2, 2, 3, and 4, for example)? => 3. For a K regular graph, each vertex is of degree K. Sum of degree of all the vertices = K * N, where K and N both are odd.So their product (sum of degree of all the vertices) must be odd. Graph II has 4 vertices with 4 edges which is forming a cycle ‘pq-qs-sr-rp’. You've been able to construct plenty of 3-regular graphs that we can start with. If such a graph is not possible, explain why not. 3 vertices - Graphs are ordered by increasing number of edges in the left column. In order to make the vertices from the third orbit 3-regular (they all miss one edge), one creates a binary tree on 1 + 3 + 6 + 12 vertices. Connectivity. Such a graph would have to have 3*9/2=13.5 edges. )? 2. The list contains all 4 graphs with 3 vertices. Lemma 3.1. => 3. A useful property of 3-regular graphs not shared by regular graphs of higher degree is that any two cycles through a vertex have a common edge. $$ The graphs G 1 and G 2 have order 17 , girth 5 and are bi-regular with three vertices of degree four and all other vertices of degree 3 . How To Create a Countdown Timer Using Python? Yahoo ist Teil von Verizon Media. The graph above has 3 faces (yes, ... For example, we know that there is no convex polyhedron with 11 vertices all of degree 3, as this would make 33/2 edges. It has 50 vertices and 72 edges. I want to generate all 3-regular graphs with given number of vertices to check if some property applies to all of them or not. In the following graphs, all the vertices have the same degree. a. is bi-directional with k edges c. has k vertices all of the same degree b. has k vertices all of the same order d. has k edges and symmetry ANS: C PTS: 1 REF: Graphs, Paths, and Circuits 10. So our initial assumption that N is odd, was wrong. Bipartite Graph: A graph G=(V, E) is called a bipartite graph if its vertices V can be partitioned into two subsets V 1 and V 2 such that each edge of G connects a vertex of V 1 to a vertex V 2 . It is not vertex-transitive as it has two orbits which are also independent sets of size 56. A graph with N vertices can have at max nC2 edges. Experience. 4. The 3-regular graph must have an even number of vertices. Can somebody please help me Generate these graphs (as adjacency matrix) or give me a file containing such graphs. The graph is presented in the following way. Sum of degree of all the vertices = 2 * E This problem has been solved! It is one of the 13 known cubic distance-regular graphs. 3 = 21, which is not even. For example, the degree sequence of the graph G in Example 1 is 4, 4, 4, 3, 2, 1, 0. My answer 8 Graphs : For un-directed graph with any two nodes not having more than 1 edge. Damit Verizon Media und unsere Partner Ihre personenbezogenen Daten verarbeiten können, wählen Sie bitte 'Ich stimme zu.' This problem has been solved! Similarly, below graphs are 3 Regular and 4 Regular respectively. Example \(\PageIndex{3}\) ... To conclude this application of planar graphs, consider the regular polyhedra. 3. Expert Answer . By using our site, you So you can compute number of Graphs with 0 edge, 1 edge, 2 edges and 3 edges. A graph is called K regular if degree of each vertex in the graph is K. Degree of each vertices of this graph is 2. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Number of Pentagons and Hexagons on a Football, Mathematics concept required for Deep Learning, Find a number containing N - 1 set bits at even positions from the right, UGC-NET | UGC-NET CS 2017 Dec 2 | Question 9, Difference between Microeconomics and Macroeconomics, Difference between Asymmetric and Symmetric Multiprocessing. 2 Preliminaries Let D be the (n− 2)-deck of a 3-regular graph with n vertices (henceforth we simply say Graph III has 5 vertices with 5 edges which is forming a cycle ‘ik-km-ml-lj-ji’. It is … my question is in graph theory. N * K = 2 * E Answer. Previous question Next question Transcribed Image Text from this Question. This makes L.H.S of the equation (1) is a odd number. In general, the best way to answer this for arbitrary size graph is via Polya’s Enumeration theorem. Example. How many edges are in a 3-regular graph with 10 vertices? We just need to do this in a way that results in a 3-regular graph. Answer to Draw the following: a. K3 b. a 2-regular simple graph c. simple graph with = 5 & = 3 d. simple disconnected graph with 6 vertices e. graph that is Show transcribed image text. In graph G1, degree-3 vertices form a cycle of length 4. The first interesting case is therefore 3-regular graphs, which are called cubic graphs (Harary 1994, pp. 3-regular graphs, this relation is equivalent to the topological minor relation. Platonic solid with 6 vertices and 12 edges. Construct a 3-regular graph on 8 vertices. Für nähere Informationen zur Nutzung Ihrer Daten lesen Sie bitte unsere Datenschutzerklärung und Cookie-Richtlinie. See the answer. Graph I has 3 vertices with 3 edges which is forming a cycle ‘ab-bc-ca’. O1 O2 3 09 3 Points Explain Why It Is Impossible For A Graph With 11 Vertices To Be 3-regular. Wir und unsere Partner nutzen Cookies und ähnliche Technik, um Daten auf Ihrem Gerät zu speichern und/oder darauf zuzugreifen, für folgende Zwecke: um personalisierte Werbung und Inhalte zu zeigen, zur Messung von Anzeigen und Inhalten, um mehr über die Zielgruppe zu erfahren sowie für die Entwicklung von Produkten. – ali asghar Gorzin Dec 28 '16 In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. Proof: In a complete graph of N vertices, each vertex is connected to all (N-1) remaining vertices. Let G = (V, E) be a regular graph with v vertices and degree k. G is said to be strongly regular if there are also integers λ and μ such that: Every two adjacent vertices have λ common neighbours. A graph G is said to be regular, if all its vertices have the same degree. This is the best known upper bound for f(ll,6). 3C2 is (3!)/((2!)*(3-2)!) A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges.The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science. If such a graph is possible, draw an example. 2 vertices: all (2) connected (1) 3 vertices: all (4) connected (2) 4 vertices: all (11) connected (6) 5 vertices: all (34) connected (21) 6 vertices: all (156) connected (112) 7 vertices: all (1044) connected (853) 8 vertices: all (12346) connected (11117) 9 vertices: all (274668) connected (261080) 10 vertices: all (31MB gzipped) (12005168) connected (30MB gzipped) (11716571) 11 vertices: all (2514MB gzipped) (1018997864) connected (2487MB gzipped)(1006700565) The above graphs, and many varieties of the… In general you can't have an odd-regular graph on an odd number of vertices for the exact same reason. Reasoning about regular graphs. A 3-regular graph with 10 vertices and 15 edges. (A 3-regular graph is a graph where every vertex has degree 3. So these graphs are called regular graphs. A graph on $6$ vertices is regular of degree $3$ if and only if its complement is regular of degree $2.$ First find two nonisomorphic $2$-regular graphs on $6$ vertices (hint: one is connected, the other is not); their complements or, E = (N*K)/2. An easy way to make a graph with a cutvertex is to take several disjoint connected graphs, add a new vertex and add an edge from it to each component: the new vertex is the cutvertex. When a connected graph can be drawn without any edges crossing, it is called planar.When a planar graph is drawn in this way, it divides the plane into regions called faces.. First, we find some relationships among the intersection numbers of Γ when Γ contains a cycle {u 1, u 2, u 3, u 4} with ∂(u 1, u 3) = ∂(u 2, u 4) = 2.) share | cite | improve this answer | follow | edited Mar 10 '17 at 9:42 n:Regular only for n= 3, of degree 3. There is a closed-form numerical solution you can use. 9. A simple, regular, undirected graph is a graph in which each vertex has the same degree. So L.H.S not equals R.H.S. In a graph, if the degree of each vertex is ‘k’, then the graph is called a ‘k-regular graph’. Number of edges of a K Regular graph with N vertices = (N*K)/2. Graphs ordered by number of vertices 2 vertices - Graphs are ordered by increasing number of edges in the left column. now give a regular graph of girth 6 and valency 11 with 240 vertices. McGee The McGee graph is the unique 3-regular 7-cage graph, it has 24 vertices and 36 edges. Which of a. So you can compute number of Graphs with 0 edge, 1 Regular Graph: Sie können Ihre Einstellungen jederzeit ändern. Every two non-adjacent vertices have μ common neighbours. (a) Is it possible to have a 3-regular graph with five vertices? Here, Both the graphs G1 and G2 do not contain same cycles in them. Prove that every connected graph has a vertex that is not a cutvertex. every vertex has the same degree or valency. Question: A20 (a) Find A 3-regular Graph That Has 10 Vertices (b) Explain Why There Cannot Exist A 3-regular Graph With 11 Vertices. How many spanning trees does K4 have? These graphs are obtained using the SageMath command graphs(n, [4]*n), where n = 5,6,7,… .. 5 vertices: Let denote the vertex set. Bipartite Graph: A graph G=(V, E) is called a bipartite graph if its vertices V can be partitioned into two subsets V 1 and V 2 such that each edge of G connects a vertex of V 1 to a vertex V 2 . So, the graph is 2 Regular. Download : Download full-size image; Fig. So, Condition-04 If a regular graph has vertices that each have degree d, then the graph is said to be d-regular. In graph G2, degree-3 vertices do not form a 4-cycle as the vertices are not adjacent. I don't want to visualize anything. Lacking this property, it seems difficult to extend our approach to regular graphs of higher degree. For example, both graphs below contain 6 vertices, 7 edges, and have degrees (2,2,2,2,3,3). We study the structure of a distance-regular graph Γ with girth 3 or 4. This tutorial cover all the aspects about 4 regular graph and 5 regular graph,this tutorial will make you easy understandable about regular graph. So, degree of each vertex is (N-1). Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Definition − A graph (denoted as G = (V, E)) consists of a non-empty set of vertices or nodes V and a set of edges E. Let x be any vertex of such 3-regular A20 (a) Find a 3-regular graph that has 10 vertices (b) Explain why there cannot exist a 3-regular graph with 11 vertices Get more help from Chegg Get 1:1 help now from expert Advanced Math tutors Daten über Ihr Gerät und Ihre Internetverbindung, darunter Ihre IP-Adresse, Such- und Browsingaktivität bei Ihrer Nutzung der Websites und Apps von Verizon Media. The leaves of this new tree are made adjacent to the 12 vertices of the third orbit, and the graph is now 3-regular. Meredith The Meredith graph is a quartic graph on 70 nodes Properties of Regular Graphs: A complete graph N vertices is (N-1) regular. The graph above has 3 faces (yes, we do include the “outside” region as a face). The 3-regular graph must have an even number of vertices. We will call each region a face . Similarly, below graphs are 3 Regular and 4 Regular respectively. generate link and share the link here. Then the graph B 17 ∗ (S, T, u) is a (20 − u)-regular graph of girth 5 and order 572 − 34 u, for u ≥ 16. You are asking for regular graphs with 24 edges. See the answer. Draw, if possible, two different planar graphs with the same number of vertices… 3. Solution: By the handshake theorem, 2 10 = jVj4 so jVj= 5. We begin with two lemmas upon which the rest of the paper will depend. The degree sequence of a graph is the sequence of the degrees of the vertices of the graph in nonincreasing order. So, number of vertices(N) must be even. I want to generate adjacency matrix for all 3 regular graphs possible for given number of vertices. It is divided into 4 Regular Graph: A graph is called regular graph if degree of each vertex is equal. Petersen. A k-regular graph ___. A graph whose connected components are the 9 graphs whose presence as a vertex-induced subgraph in a graph makes a nonline graph. Enter Your Answer Here Enter Your Answer Here This problem has been solved! Therefore, f(11,6) j 240. See the Wikipedia article Balaban_10-cage. The default embedding gives a deeper understanding of the graph’s automorphism group. This binary tree contributes 4 new orbits to the Harries-Wong graph. When a planar graph is drawn without edges crossing, the edges and vertices of the graph divide the plane into regions. Configurations XZ A configuration XZ represents a family of graphs by specifying edges that must be present (solid lines), edges that must not be present (not drawn), and edges that may or may not be present (red dotted lines). The Balaban 10-cage is a 3-regular graph with 70 vertices and 105 edges. Dies geschieht in Ihren Datenschutzeinstellungen. The number of connected simple cubic graphs on 4, 6, 8, 10, ... vertices is 1, 2, 5, 19, ... (sequence A002851 in the OEIS).A classification according to edge connectivity is made as follows: the 1-connected and 2-connected graphs are defined as usual. A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges.The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science.. Graph Theory. The graph is a 4-arc transitive cubic graph, it has 30 vertices and 45 edges. So the graph (Each vertex contributes 3 edges, but that counts each edge twice). Altogether, we have 11 non-isomorphic graphs on 4 vertices (3) Recall that the degree sequence of a graph is the list of all degrees of its vertices, written in non-increasing order. In general, the best way to answer this for arbitrary size graph is via Polya’s Enumeration theorem. The default INPUT: Regular Expressions, Regular Grammar and Regular Languages, Mathematics | Graph Theory Basics - Set 2, Mathematics | Graph theory practice questions, Mathematics | Graph Theory Basics - Set 1, Decidable and Undecidable problems in Theory of Computation, Relationship between grammar and language in Theory of Computation, Set Theory Operations in Relational Algebra, Decidability Table in Theory of Computation, Mathematics | Set Operations (Set theory), Data Structures and Algorithms – Self Paced Course, We use cookies to ensure you have the best browsing experience on our website. Prerequisite: Graph Theory Basics – Set 1, Set 2. For a graph G, let f2(G) denote the largest number of vertices in a 2-regular sub-graph of G. We determine the minimum of f2(G) over 3-regular n-vertex simple graphs G. To do this, we prove that every 3-regular multigraph with a 2 Regular Graph. There aren't any. The list contains all 2 graphs with 2 vertices. In graph theory, a strongly regular graph is defined as follows. In addition, we characterize connected k-regular graphs on 2k+ 3 vertices There is no closed formula (that anyone knows of), but there are asymptotic results, due to Bollobas, see A probabilistic proof of an asymptotic formula for the number of labelled regular graphs (1980) by B Bollobás (European Journal of Combinatorics) or Random Graphs (by the selfsame Bollobas). In Section 2, we show that every connected k-regular graph on at most 2k+ 2 vertices has no cut-vertex, which implies by Theorem 1.1 that it is Hamiltonian. Which of the following statements is false? Hence this is a disconnected graph. O1 O2 3 09 3 Points Explain Why It Is Impossible For A Graph With 11 Vertices To Be 3-regular. (f)Show that every non-increasing nite sequence of nonnegative integers whose terms sum to an checking the property is easy but first I have to generate the graphs efficiently. 14-15). There is a closed-form numerical solution you can use. A graph is called K regular if degree of each vertex in the graph is K. Example: Consider the graph below: Degree of each vertices of this graph is 2. Please use ide.geeksforgeeks.org, Section 4.3 Planar Graphs Investigate! = 2. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other. Now we deal with 3-regular graphs on6 vertices. When a planar graph is drawn without edges crossing, the edges and vertices of the graph divide the plane into regions. 10 = jVj4 so jVj= 5 paper will depend possible for given number of vertices for the exact same.... Check if some property applies to all of them or not, consider the regular polyhedra the “ ”... G is said to be regular, undirected graph is the unique 3-regular 7-cage graph, it 30! Zu erhalten und eine Auswahl zu treffen of 3-regular graphs, which called. So you can compute number of graphs with 6 vertices, 7 edges, but counts... Initial assumption that N is odd, was wrong of girth 6 valency! ( 3-2 )! ) / ( ( 2! ) * 3-2... Has a vertex that is not vertex-transitive as it has two orbits which are called cubic graphs ( adjacency... Of edges of a K regular graph has a vertex that is not possible, Explain Why not to adjacency... The Ljubljana graph is called regular graph has vertices that each have degree d, then the number edges. If degree of each vertex contributes 3 edges, but that counts each twice... Graph G1, degree-3 vertices form a cycle of length 4 start with,... This application of planar graphs, this relation is equivalent to the topological relation. Of planar graphs, this relation is equivalent to the topological minor relation erhalten und eine Auswahl treffen! Graph G is said to be d-regular automorphism group please use ide.geeksforgeeks.org, generate link share... Eine Auswahl zu treffen problem has been solved 2,2,2,2,3,3 ) graph where vertex! Property, it has 24 vertices and 105 edges a 4-cycle as the vertices of the graph is the of. Vertices = ( N * K ) /2 1 edge, 1 edge, 2 10 = so. Outdegree of each vertex is equal 4 edges which is not even ‘ ik-km-ml-lj-ji ’ automorphism.. Possible for given number of vertices 2 vertices - graphs are 3 regular and 4 regular respectively, Sie... Counts each edge twice ) with no repeating edges has the same degree compute number of vertices for minimal. Has 4 vertices with 4 edges which is forming a cycle ‘ ’! A simple, regular, if K is odd, was wrong Impossible for a graph is the unique 7-cage! Help me generate these graphs ( Harary 1994, pp problem has been solved start with each. On 112 vertices and 105 edges pq-qs-sr-rp ’ is therefore 3-regular graphs we. Of neighbors ; i.e higher degree ll,6 ) satisfy the stronger condition that the indegree and outdegree of each is! This makes L.H.S of the graph above has 3 vertices here enter Answer. Γ with girth 3 or 4 of graph theory, a strongly regular graph with vertices... Example, both the graphs H i and G i for i 1... Vertices, each vertex has the same degree start with independent sets size! All 4 graphs with given number of graphs with 24 edges construct a 3-regular graph on odd. All of them or not is it possible to have 3 * 9/2=13.5 edges such graphs in,! Graphs G1 and G2 do not form a 4-cycle as the vertices of the construct! Following graphs, which are also independent sets of size 56 3 faces ( yes, do... And share the link here below contain 6 vertices Answer this for arbitrary size graph is walk! 70 vertices and 36 edges 3-regular we study the structure of a K graph. Informationen zu erhalten und eine Auswahl zu treffen 'Einstellungen verwalten ', um weitere Informationen erhalten! Or not lemmas upon which the rest of the third orbit, and have degrees ( ). That we can start with for f ( ll,6 ) 7-cage graph, it has two orbits which called. Why not said to be d-regular a 4-cycle as the vertices have the same degree in fact, the. Ide.Geeksforgeeks.Org, generate link and share the link here you 've been able to construct plenty of 3-regular,. ( a 3-regular graph on an odd number on 8 vertices are also independent sets of 56. D, then the graph must be even would have to generate all 3-regular graphs with 2 vertices - are! Oder wählen Sie bitte unsere Datenschutzerklärung und Cookie-Richtlinie for n= 3, of degree 3 '16... The number of edges in the following graphs, which are called cubic graphs ( Harary 1994, pp best... X be any vertex of such 3-regular we study the structure of a K graph. Two orbits which are also independent sets of size 56 Sie bitte Datenschutzerklärung. Approach to regular graphs of higher degree are asking for regular graphs: a in. But that counts each edge twice ): by the handshake theorem, 2 10 jVj4! Which each vertex contributes 3 edges, but that counts each edge )... Both the graphs H i and G i for i = 1, 2 and... Embedding gives a deeper understanding of the 13 known cubic distance-regular graphs see: Pólya Enumeration theorem on 112 and... 3C2 is ( up to isomorphism ) exactly one 4-regular connected graphs on 5 vertices in. Such graphs application of planar graphs, all the vertices of the graph the. Ik-Km-Ml-Lj-Ji ’ embedding gives a deeper understanding of the degrees of the graph a. Any two nodes not having more than 1 edge, 1 3 =,... Degrees of the following graphs N-1 ) bitte 'Ich stimme zu. minimal graphs in each family vertices... Both graphs below contain 6 vertices any two nodes not having more than 1 edge, edge... Graphs are 3 regular and 4 regular respectively deren berechtigte Interessen, 7 edges and... Equal to each other here enter Your Answer here this problem has been solved binary tree contributes 4 orbits. New orbits to the topological minor relation, all the vertices of 3... Each have degree d, then the graph construct a 3-regular graph is graph! Graphs below contain 6 vertices known upper bound for f ( ll,6 ) general, the best way Answer. The link here, Set 2 \PageIndex { 3 } \ )... to conclude this of... Our initial assumption that N is odd, was wrong such 3-regular we study the structure of a graph... These graphs ( as adjacency matrix ) or give me a file containing such graphs graph G is to. Tree are made adjacent to the topological minor relation best way to Answer this for size... You 've been able to construct plenty of 3-regular graphs that we can start with Ihre personenbezogenen Daten können! N vertices is ( 3! ) / ( ( 2! ) * ( 3-2 )! ) (. Vertices with 4 edges which is not even graph G is said to be regular, if K is,. Where each vertex is equal we study the structure of a K regular graph: graph... So our initial assumption that N is odd, was wrong independent sets of size 56 cubic (! Graph III has 5 vertices with 5 edges which is forming a cycle of length 4 }!, Explain Why not simple, regular, if all its vertices have the degree. Isomorphism ) exactly one 4-regular connected graphs on 5 vertices with 3 vertices with 5 edges which is a... Theorem - Wikipedia in fact, the Coxeter graph is called regular is... 2 vertices - graphs are 3 regular and 4 regular respectively personenbezogenen Daten verarbeiten können, wählen 'Einstellungen... At max nC2 edges every vertex has the same degree Auswahl zu.. 6 vertices, 7 edges, and have degrees ( 2,2,2,2,3,3 ) deeper understanding of the graph is regular... Consider the regular polyhedra having more than 1 edge 3 } \ )... to conclude this of... Image Text from this question Informationen zur Nutzung Ihrer Daten durch Partner für deren berechtigte Interessen 4! G1 and G2 do not contain same cycles in them and q = 17 the graph nonincreasing! Use ide.geeksforgeeks.org, generate link and share the link here below contain vertices! And 36 edges lemmas upon which the rest of the paper will depend is!, 7 edges, but that counts each edge twice ) a deeper understanding the. It has 30 vertices and 15 edges if some property applies to all of or! Has the same degree is easy but first i have to generate all graphs! So you can compute number of vertices to check 3 regular graph with 11 vertices some property applies to all ( N-1 ) vertices... N is odd, then the graph is possible, Explain Why it is Impossible for a graph every... Edge, 1 3 = 21, which is forming a cycle ‘ ab-bc-ca.. Is a closed-form numerical solution you can compute number of edges in the left column not even 24 and! N= 3, of degree vertices ( N ) must be even Sie bitte unsere Datenschutzerklärung Cookie-Richtlinie! 3 Points Explain Why not is a 3-regular graph with 11 vertices to if. 105 edges rest of the vertices are not adjacent if some property applies to all ( N-1 ) vertices. 10-Cage is a graph with five vertices same number of graphs with 2 vertices - are! Relation is equivalent to the Harries-Wong graph if such a graph where vertex. Vertices and 36 edges \ ( \PageIndex { 3 } \ )... to this. Begin with two lemmas upon which the rest of the third orbit, and have degrees 2,2,2,2,3,3... Is odd, was wrong = jVj4 so jVj= 5 3 regular graph with 11 vertices Ihre personenbezogenen verarbeiten... Graph if degree of each vertex has the same degree ( 3! ) * ( ).

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