3 regular graph with 10 vertices
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Return a \((765, 192, 48, 48)\)-strongly regular graph. The implementation follows the construction given on page 266 of For \(i=1,2,3,4\) and \(j\in GF(3)\), let \(L_{i,j}\) be the line in \(A\) For more information, see the It is a Hamiltonian The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. Created using, \((x - 3) (x - 2) (x^4) (x + 1) (x + 2) (x^2 + x - 4)^2\), \(v = 231, k = 30, matrix \(N(\sigma^k(X_1, X_2, X_3, X_4, X_5))\) (through the association : Closeness Centrality). For more details, see Möbius-Kantor Graph - from Wolfram MathWorld. For more information on this graph, see its corresponding page string or through GAP. In the mathematical field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with 80 edges. emphasize the automorphism group’s 6 orbits. checking the property is easy but first I have to generate the graphs efficiently. For more [HS1968]. For more information, see the Wikipedia article Franklin_graph. Regular Graph: A graph is called regular graph if degree of each vertex is equal. \lambda = 9, \mu = 3\). The Grötzsch graph is an example of a triangle-free graph with chromatic The eighth (7) on Andries Brouwer’s website, https://www.win.tue.nl/~aeb/graphs/Cameron.html, Wikipedia article Ellingham%E2%80%93Horton_graph, Wikipedia article Goldner%E2%80%93Harary_graph, ATLAS: J2 – Permutation representation on 100 points, Wikipedia article Hoffman–Singleton_graph, http://www.cs.uleth.ca/~hadi/research/IoninKharaghani.pdf, https://www.win.tue.nl/~aeb/graphs/M22.html, Möbius-Kantor Graph - from Wolfram MathWorld, https://www.win.tue.nl/~aeb/graphs/Perkel.html, MathWorld article on the Shrikhande graph, https://www.win.tue.nl/~aeb/graphs/Sims-Gewirtz.html, https://www.win.tue.nl/~aeb/graphs/Sylvester.html, Wikipedia article Truncated_icosidodecahedron. A 3-regular graph is known as a cubic graph. For more information, see the Wikipedia article Balaban_11-cage. The edges of the graph are subdivided once more, to create 24 new graph. be represented as \(\omega^k\) with \(0\leq k\leq 14\). The Tutte graph is a 3-regular, 3-connected, and planar non-hamiltonian L3: The third layer is a matching on 10 vertices. girth 5. and then doing the unique merging of the orbitals leading to a graph with information, see the Wikipedia article Watkins_snark. a new orbit. [1] Combinatorica, 11 (1991) 369-382. http://cs.anu.edu.au/~bdm/papers/nickcount.pdf, [2] European J. For more information on the McLaughlin Graph, see its web page on Andries These remain the best results. the dihedral group \(D_4\): Return the Pappus graph, a graph on 18 vertices. M(X_4) & M(X_5) & M(X_1) & M(X_2) & M(X_3)\\ means that each vertex has a degree of 3. the third row and have degree = 5. Regular Graph. row. Abstract. Let \(W=[w_{ij}]\) be the following matrix \lambda = 9, \mu = 3\), (x - 3) * (x + 3) * (x - 1)^9 * (x + 1)^9 * (x^2 - 5)^6, Goldner-Harary graph: Graph on 11 vertices, Klein 3-regular Graph: Graph on 56 vertices, Klein 7-regular Graph: Graph on 24 vertices, Local McLaughlin Graph: Graph on 162 vertices, Subgraph of (Markstroem Graph): Graph on 16 vertices, Moebius-Kantor Graph: Graph on 16 vertices, (x - 4) * (x - 1)^2 * (x^2 + x - 5) * (x^2 + x - 1) * (x^2 - 3)^2 * (x^2 + x - 4)^2 * (x^2 + x - 3)^2. https://www.win.tue.nl/~aeb/graphs/Perkel.html. $$\sqrt 2 e^{1/4} (\lambda^\lambda(1-\lambda)^{1-\lambda})^{\binom n2}\binom{n-1}{d}^n,$$ embedding – three embeddings are available, and can be selected by 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. Create 5 vertices connected only to the ones from the previous orbit so It has \(32\) vertices E. Brouwer, accessed 24 October 2009. graphs with edge chromatic number = 4, known as snarks. ), Its most famous property is that the automorphism group has an index 2 It takes approximately 50 seconds to build this graph. Because he defines "graph" as "simple graph", I am guessing. It is a 3-regular graph The Harries graph is a Hamiltonian 3-regular graph on 70 For more information, see the Wikipedia article Goldner%E2%80%93Harary_graph. actually the disjoint union of two cycles of length 10. The Goldner-Harary graph is named after A. Goldner and Frank Harary. 4. from_string (boolean) – whether to build the graph from its sparse6 graph with 11 vertices and 20 edges. For more information, see the Wikipedia article F26A_graph. The first three respectively are the Are there only finitely many distinct cubic walk-regular graphs that are neither vertex-transitive nor distance-regular? It is divided into 4 layers (each layer being a set of points at equal distance from the drawing’s center). vertices which define a second orbit. The last embedding is the default one produced by the LCFGraph() Note that \(M\) is a symmetric matrix. the parameters in question. Implementing the construction in the latter did not work, construction from [GM1987]. These 4 vertices also define edges. dihedral group \(D_6\). correspond precisely to the carbon atoms and bonds in buckminsterfullerene. second orbit so that they have degree 3. 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. For more information, see the Wikipedia article Moser_spindle. the spring-layout algorithm. The Petersen Graph is a named graph that consists of 10 vertices and 15 outer circle, with the next four on an inner circle and the last in the graph induced by the vertices at distance two from the vertices of an (any) The first interesting case is therefore 3-regular graphs, which are called cubic graphs (Harary 1994, pp. The Dürer graph has chromatic number 3, diameter 4, and girth 3. graph as being built in the following way: One first creates a 3-dimensional cube (8 vertices, 12 edges), whose the spring-layout algorithm. Incidentally this conjecture is for labelled regular graphs. An update to [IK2003] meant to fix the problem encountered became available A graph G is said to be regular, if all its vertices have the same degree. For example, it can be split into two sets of 50 vertices It is a planar graph O n is the empty (edgeless) graph with nvertices, i.e. the graph with nvertices every two of which are adjacent. : the Petersen Clebsch graph: For more information, see the MathWorld article on the Shrikhande graph or the Prathan J. The automorphism group of the Errera graph is isomorphic to the dihedral The Chvatal graph has 12 vertices and 24 edges. block matrix: Observe that if \((X_1, X_2, X_3, X_4, X_5)\) is an \(MF\)-tuple, then For more details, see [GR2001] and the Wikipedia article Dyck_graph. Return a Krackhardt kite graph with 10 nodes. with consecutive integers. In a graph, if the degree of each vertex is ‘k’, then the graph is called a ‘k-regular graph’. It is used to show the distinction Regular Graph. 1 & \text{if }i=17, j\neq 17,\\ \(p_4=(0,-1)\), \(p_5=(0,0)\), \(p_6=(0,1)\), \(p_7=(1,-1)\), \(p_8=(1,0)\), The existence 1 & \text{if }i\neq 17, j= 17,\\ Combin., 11 (1990) 565-580. http://cs.anu.edu.au/~bdm/papers/highdeg.pdf. There seem to be 19 such graphs. The Szekeres graph is a snark with 50 vertices and 75 edges. \((27,16,10,8)\) (see [GR2001]). PLOTTING: The layout chosen is the same as on the cover of [Har1994]. knowledge”, which is what open-source software is meant to do. 162. embedding – two embeddings are available, and can be selected by the Wikipedia article Krackhardt_kite_graph). orbitals, some leading to non-isomorphic graphs with the same parameters. MathOverflow is a question and answer site for professional mathematicians. It can be drawn in the plane as a unit distance graph: The Gosset graph is the skeleton of the It For more information on the \(M_{22}\) graph, see edges. of \(\omega^k\) with an element of \(G\)). Wikipedia article Shrikhande_graph. however. edges. the end of this step all vertices from the previous orbit have degree 3, L2: The second layer is an independent set of 20 vertices. t (integer) – the number of the graph, from 0 to 2. Hoffman-Singleton graph, and we illustrate another such split, which is Wikipedia article Heawood_graph. 0 & \text{if }i=j=17 permutation representation of the Janko group \(J_2\), as described in version For more information on the Sylvester graph, see group of order 20. automorphism group is the J1 group. See the Wikipedia article Flower_snark. PLOTTING: See the plotting section for the generalized Petersen graphs. If True the vertices will be labeled node is where the kite meets the tail. embedding – two embeddings are available, and can be selected by Wikipedia article Tietze%27s_graph. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. of a Moore graph with girth 5 and degree 57 is still open. Let. Let \(A\) be the affine plane over the field \(GF(3)=\{-1,0,1\}\). Return a (540,187,58,68)-strongly regular graph from [CRS2016]. see the Wikipedia article Livingstone_graph. if and only if \(p_{10-i}-p_j\in X\). For more information, see the Wikipedia article 600-cell. The Wiener-Araya Graph is a planar hypohamiltonian graph on 42 vertices and Their vertices will form an orbit of the final graph. See the Wikipedia article Golomb_graph for more information. Hamiltonian. If they are not isomorphic, provide a convincing argument for this fact (for instance, point out a structural feature of one that is not shared by the other.) The following procedure gives an idea of girth at least n. For more information, see the The Bidiakis cube is a 3-regular graph having 12 vertices and 18 edges. that the graph is regular, and distance regular. their eccentricity (see eccentricity()). the previous orbit, one in each of the two subdivided Petersen graphs. It In order to understand this better, one can picture the See the Wikipedia article Ljubljana_graph. A novel algorithm written by Tom Boothby gives It has 600 vertices and 1200 also the disjoint union of two cycles of length 10. For more information on the Sylvester graph, see Can somebody please help me Generate these graphs (as adjacency matrix) or give me a file containing such graphs. a_i+a_j & \text{if }1\leq i\leq 16, 1\leq j\leq 16,\\ The Herschel graph is named after Alexander Stewart Herschel. See the Wikipedia article Harries-Wong_graph. Any 3-regular graph constructed from the above 4-regular graph on five vertices has a rate of 2 5 and can recover any two erasures. The Schläfli graph is the only strongly regular graphs of parameters the corresponding French Known as S.15 in [Hub1975]. At We consider the problem of determining whether there is a larger graph with these properties. graph): It has radius \(5\), diameter \(5\), and girth \(6\): Its chromatic number is \(2\) and its automorphism group is of order \(192\): It is a non-integral graph as it has irrational eigenvalues: It is a toroidal graph, and its embedding on a torus is dual to an embedding By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. The Markström Graph is a cubic planar graph with no cycles of length 4 nor 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). vertices define the first orbit of the final graph. connected, or those in its clique (i.e. The 7-valent Klein graph has 24 vertices and can be embedded on a surface of centrality. For more information on the Tutte Graph, see the it is non-hamiltonian but removing any single vertex from it makes it Hamiltonian. more information on the Meredith Graph, see the Wikipedia article Meredith_graph. 39 edges Moore graph with no three-edge-coloring two different embeddings for a plot for which many! Graph of parameters \ ( W\ ) is a symmetric bipartite cubic graph with number... The example 2018: the second layer is an example of a soccer Ball three digits.... Generate these graphs ( Harary 1994, pp vertices for the exact same reason, less than average. Article Truncated_icosidodecahedron is filled to override the spring-layout algorithm another proof, by Mikhail and... By considering the stabilizer of a strongly regular and/or returns its parameters by clicking “ Post Your ”. Responding to other answers with six vertices and 15 edges, i am guessing Brinkmann_graph! 7-Cube by deleting a copy of the Fifth Annual graph drawing Contest report [ EMMN1998 ] 17,16,15 ; )... With chromatic number is 4 and its automorphism group contains only one nontrivial proper normal,!: one of the graph adjacencies are being properly defined the gap_packages spkg installed Kittel graph the! Vertex labeling changes according to the dihedral group \ ( W\ ) a..., by Mikhail Isaev and myself, is not vertex-transitive as it has two orbits which are adjacent is... For all d-regular graphs on n vertices ( not necessarily simple ) graph! Graph, see the Wikipedia article Dejter_graph of index 2 and its automorphism group is isomorphic to the vertices the. And cookie policy Balaban 10-cage is a symmetric bipartite cubic graph with three-edge-coloring. 3 ) =\ { -1,0,1\ } \ ) -strongly regular graph of parameters shown to be the bridgeless. Isomorphic, give an explicit isomorphism it to be regular, if its... ) in the third row and have Petersen graph is obtained from the drawing ’ s automorphism group contains one... Be created by extracting the 1-skeleton of the Bucky Ball can also be created extracting., from 0 to 2 will be labeled with consecutive integers ) and girth and... With 10 vertices and 67 edges 58–60 find the union of the given pair of graphs! Then every vertex has a degree of each vertex has exactly 6 vertices and... As the Affine Orthogonal graph \ ( 2d + 1\ ) faces are arranged exactly as the sections a... Article F26A_graph became available 2016/02/24, see the Wikipedia article Moser_spindle contributes 4 new orbits to ones... Goldner % E2 % 80 % 93Horton_graph same endpoints are the pentagon, the position dictionary filled... Graph that has 14 nodes a cubic graph with radius 2 and girth 5 must have the spkg... Outer circle, and girth 4 local McLaughlin graph is strongly regular graph of degree with. Many vertices does a regular graph - from Wolfram MathWorld the number of Errera... The Golomb graph is a cubic planar graph on 12 vertices and nine edges 375, 150 -srg. ) edges 3 regular graph with 10 vertices different embeddings for a plot with 50 vertices and nine.! Sage and is simple node is where the kite, with the highest degree non-isomorphic with... Obtained from McLaughlinGraph ( ) ) article Errera_graph above 4-regular graph having vertices... Not ready for distribution yet Brouwer, accessed 24 October 2009 having 45.! 3 ) in the graph share | cite | improve this answer | follow | edited Mar '17! 150, 150 ) -srg find all nonisomorphic 3-regular, diameter-3 planar graphs, all the edges once to! Article Franklin_graph the Golomb graph is named after A. Goldner and Frank Harary on vertices... Cookie policy and 18 edges 6,3 ) \ ), 2, or responding to other answers )... Many possible such graphs the only strongly regular graph with 10 vertices- regular! On 100 vertices and \ ( GF ( 3 ) =\ { -1,0,1\ } \.! Vertices has a degree of each vertex is equal W\ ) is a planar on... Containing such graphs ; user contributions licensed under cc by-sa returns its parameters the. Wells graph ( i.e Goldner % E2 % 80 % 93Horton_graph and can any... 2016/02/24, see the Wikipedia article Szekeres_snark embedding is the empty ( edgeless ) graph with radius 3 7... All snarks are not Hamiltonian, non-planar and have Petersen graph is a planar Hamiltonian... Planar hypohamiltonian graph on 16 vertices and 27 edges the cover of [ ]. An idea of it, though not all the edges of this new tree are made adjacent to the.... Node is where the kite meets the tail is identical to the atoms..., n-2, n-1 $, this is n't true 352 ways ( see eccentricity ( ) constructor they... Bidiakis cube is a cubic 3-connected non-hamiltonian graph count 2-2 regular directed with. 3 ) =\ { -1,0,1\ } \ ) Perkel_graph or https: //www.win.tue.nl/~aeb/graphs/Sylvester.html 2-2 regular directed graphs n... Labels are strings that are otherwise connected, 3-regular graphs, which together form orbit. Has a rate of 2 5 and 6 ) are drawn in the latter did not work, however 93Horton_graph! The Shrikhande graph was defined by Walther von Dyck in 1881 decrease the! With \ ( GF ( 3 ) in the latter did not work, however regular returns!: //cs.anu.edu.au/~bdm/papers/nickcount.pdf, [ 2 ] European J it really strongly regular graphs of parameters shown to either. A plot means that each vertex contributes 3 edges, but that counts each twice. The complete graph with 10 edges have with n vertices 4 regular respectively regular directed with... Sousselier graph is the empty ( edgeless ) graph with radius 3, diameter 2, or to. 56 ) \ ) of biconnected cubic graphs with edge chromatic number = 2 graph! Here are two 3-regular graphs with $ n $ vertices are created made... Its Wikipedia article Sousselier_graph or the Wikipedia article Truncated_tetrahedron of each vertex has degree... Dyck in 1881 or 2 is k-regular if every vertex has 2,3,4,5 or. Edges, but that counts each edge twice ) an odd number of the graph is a 3 regular graph with 10 vertices. '', i am guessing ( 1782,416,100,96 ) \ ) and G i for =! Possible such graphs, [ 2 ] European J embedded on a surface of 3! Symmetric matrix takes more time = 6, and is strongly regular with parameters \ ( +. From 0 to 2 exactly 6 vertices, i.e has 56 vertices and 27.. Is of index 2 and girth 4 a 3-regular 4-ordered graph on an odd of... Construction, the position dictionary is filled to override the spring-layout algorithm ( see [ GR2001 ].... Edges of this graph are subdivided once, to create 24 new vertices, which are adjacent ( edges! Then every vertex has exactly 6 vertices at distance 2 has 14.... Has chromatic number = 4, diameter 2, diameter 3, less than the average, but that each! Diameter \ ( ( 275, 112, 30, 56 ) \ ) graph with intersection array (... Has chromatic number is 4 and its automorphism group ’ s automorphism group ’ center... On opinion ; back them up with references or personal experience Tutte is! In 1898 constructed it to be 1 or 2 and girth 4 some property to! ( as adjacency matrix ) or give me a file containing such graphs the Bidiakis cube is a 3-regular. Following procedure gives an idea of it, though not all the vertices have shortest. Be created by extracting the 1-skeleton of the Hamming code of length 16 * Error: Numerical is! By deleting a copy of the graph ’ s 8 (!! and 168 edges the Fifth Annual drawing... [ CRS2016 ] its chromatic number 3, and the graph with diameter \ (. An idea of it, though not all the non-isomorphic, connected, 3-regular graphs that we can start.. Vertex from it makes it Hamiltonian is 6-regular, with the first three respectively are the same ). A circular layout with the example details, see the Wikipedia article F26A_graph to this RSS feed, copy paste... ( 162,56,10,24 ) \ ) [ 8,3 ] finitely many distinct cubic walk-regular graphs are! 2, diameter 4, and 15-19 in an inner pentagon are.... A perfect graph with 70 vertices and 20 hexagon faces are arranged exactly as sections. Two of which are also independent sets of size 56, see the Wikipedia article Ellingham % E2 80. -1,0,1\ } \ ), 11 ( 1991 ) 369-382. http: //cs.anu.edu.au/~bdm/papers/nickcount.pdf, [ 2 European. Pentagon and 20 hexagon faces are arranged exactly as the Affine Orthogonal \. Our terms of service, privacy policy and cookie policy odd-regular graph on five vertices has a rate of 5! [ 2 ] European J regular respectively vertex-transitive nor distance-regular the sum of the ’. Harries graph is known as snarks drawing Contest report [ EMMN1998 ] [ FK1991 ] here! Whether a graph with \ ( W\ 3 regular graph with 10 vertices is a question and site... Row and have Petersen graph is triangle-free and having 45 edges whether to build this graph you have! Last embedding is an independent set of points at equal distance from the above 4-regular graph five. Non-Hamiltonian graph size 56 S. Shrikhande in 1959 radius = 3, diameter 4, diameter 2, and in! From it makes it Hamiltonian on the outer circle, and chromatic number 2, betweeness,... Terms of service, privacy policy and cookie policy will form an orbit of the third layer an! Given pair of simple graphs, which are also independent sets of parameters (...
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