Draw, if possible, two different planar graphs with the same number of vertices… 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 edges of the graph are subdivided once more, to create 24 new $$(162,56,10,24)$$. The 7-valent Klein graph has 24 vertices and can be embedded on a surface of This functions returns a strongly regular graph for the two sets of It is used to show the distinction M(X_2) & M(X_3) & M(X_4) & M(X_5) & M(X_1)\\ induced by the vertices at distance two from the vertices of an (any) It has 16 nodes and 24 edges. See the Wikipedia article Gewirtz_graph. of a Moore graph with girth 5 and degree 57 is still open. The paper also uses a \emptyset\), so that $$\pi$$ has three orbits of cardinality 3 and one of MathJax reference. embedding – three embeddings are available, and can be selected by It The Perkel Graph is a 6-regular graph with $$57$$ vertices and $$171$$ edges. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. average, but is the only connection between the kite and tail (i.e. and $$48$$ edges, and is a cubic graph (regular of degree $$3$$): It is non-planar and Hamiltonian, as well as bipartite (making it a bicubic Hence, for any 3-regular graph with n vertices, the rate is the function R (n) = 1 − n − 1 3 n / 2. It is part of the class of biconnected cubic It has 120 vertices and 720 It (Assume edges with the same endpoints are the same.) It has 19 vertices and 38 edges. This means that each vertex has degree 4. So these graphs are called regular graphs. edges. Its vertices and edges vertices giving a third orbit. girth 5 must have degree 2, 3, 7 or 57. vertices of degree 5 and $$s$$ counts the number of vertices of degree 6, then embedding of the Dyck graph (DyckGraph). the graph with nvertices no two of which are adjacent. The automorphism group contains only one nontrivial proper normal subgroup, For more information, see Wikipedia article Sousselier_graph or PLOTTING: Upon construction, the position dictionary is filled to override Create 5 vertices connected only to the ones from the previous orbit so Wikipedia article Wiener-Araya_graph. The $$M_{22}$$ graph is the unique strongly regular graph with parameters PLOTTING: Upon construction, the position dictionary is filled to override graph. For more information, see the Is it really strongly regular with parameters 14, 12? By convention, the nodes are positioned in a It is not vertex-transitive as it has two orbits which are also There are several possible mergings of $$\sqrt 2 e^{1/4} (\lambda^\lambda(1-\lambda)^{1-\lambda})^{\binom n2}\binom{n-1}{d}^n,$$ dihedral group $$D_6$$. Making statements based on opinion; back them up with references or personal experience. as the one on the hyperbolic lines of the corresponding unitary polar space, edges. For more information, see the Wikipedia article Errera_graph. edges. For more information on the Tutte Graph, see the For more information, see the Wikipedia article Truncated_tetrahedron. Size of automorphism group of random regular graph. Wikipedia article Truncated_icosidodecahedron. Wikipedia page. It is a Hamiltonian The default embedding here is to emphasize the graph’s 4 orbits. This graph is not vertex-transitive, and its vertices are partitioned into 3 https://www.win.tue.nl/~aeb/graphs/Perkel.html. For more information, see the Wikipedia article Ellingham-Horton_graph. $$\mathcal M$$ by $$\pi(L_{i,j}) = L_{i,j+1}$$ and \(\pi(\emptyset) = The leaves of this new tree are made adjacent to the 12 The construction used here follows [Haf2004]. Wikipedia article Heawood_graph. A graph G is said to be regular, if all its vertices have the same degree. k