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A quartic vertex-transitive graph is a quartic graph that is vertex transitive. Read and Wilson (1988, pp. 164-166) enumerate all connected quartic vertex-transitive graphs ...

A quasi-qunitic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 ...

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 ...

A directed strongly regular graph is a simple directed graph with adjacency matrix A such that the span of A, the identity matrix I, and the unit matrix J is closed under ...

The skeleton graphs of the Johnson solids are polyhedral graphs. The Johnson skeleton graphs J_3 and J_(63) are minimal unit-distance forbidden graphs. The skeleton of the ...

A Moore graph of type (v,g) is a regular graph of vertex degree v>2 and girth g that contains the maximum possible number of nodes, namely ...

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

A simple unlabeled graph whose connectivity is considered purely on the basis of topological equivalence, so that two edges (v_1,v_2) and (v_2,v_3) joined by a node v_2 of ...

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...

A uniquely Hamiltonian graph is a graph possessing a single Hamiltonian cycle. Classes of uniquely Hamiltonian graphs include the cycle graphs C_n, Hanoi graphs H_n, ladder ...