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The Ionin-Kharaghani graph is a strongly regular graph on 765 vertices and 73440 edges. It has regular parameters (nu,k,lambda,mu)=(765,192,48,48). It is implemented in the ...

The cube-connected cycle graph of order n is the graph obtained by replacing each vertex in a n-dimensional hypercube by a cycle of length n. They were introduced by ...

Isomorphic factorization colors the edges a given graph G with k colors so that the colored subgraphs are isomorphic. The graph G is then k-splittable, with k as the divisor, ...

There appears to be no term in standard use for a graph with graph crossing number 1. Furthermore, the terms "almost planar" and "1-planar" are used in the literature for ...

The cubeplex graph is the cubic Hamiltonian graph on 12 nodes illustrated above in several embeddings and corresponding to the graph Gamma_1 in Fischer and Little (2001). It ...

The Ljubljana graph is a graph on 112 vertices that is the third smallest cubic semisymmetric graph. It was discovered by Brouwer et al. (1993) and rediscovered by Conder et ...

A polyhedral nonhamiltonian graph is a graph that is simultaneously polyhedral and nonhamiltonian. The smallest possible number of vertices a nonhamiltonian polyhedral graph ...

A spider graph, spider tree, or simply "spider," is a tree with one vertex of degree at least 3 and all others with degree at most 2. The numbers of spiders on n=1, 2, ... ...

The Kneser graphs are a class of graph introduced by Lovász (1978) to prove Kneser's conjecture. Given two positive integers n and k, the Kneser graph K(n,k), often denoted ...

The star graph S_n of order n, sometimes simply known as an "n-star" (Harary 1994, pp. 17-18; Pemmaraju and Skiena 2003, p. 248; Tutte 2005, p. 23), is a tree on n nodes with ...