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The smallest possible number of vertices a polyhedral nonhamiltonian graph can have is 11, and there exist 74 such graphs, including the Herschel graph and the Goldner-Harary ...

An apex graph is a graph possessing at least one vertex whose removal results in a planar graph. The set of vertices whose removal results in a planar graph is known as the ...

A graph that can be reduced to another graph with the same degree sequence by edge-switching is known as a switchable graph. Conversely, a graph that cannot be reduced to ...

The double graph of a given graph G is constructed by making two copies of G (including the initial edge set of each) and adding edges u_1v_2 and v_1u_2 for every edge uv of ...

Rubik's graph is the Cayley graph of Rubik's group. The graph diameter of this graph is sometimes known as God's number, and was shown in Aug. 2010 to be equal to 20 (Rokicki ...

In graph theory, a cycle graph C_n, sometimes simply known as an n-cycle (Pemmaraju and Skiena 2003, p. 248), is a graph on n nodes containing a single cycle through all ...

There are several differing definitions of the sun graph. ISGCI defines a (complete) n-sun graph as a graph on 2n nodes (sometimes also known as a trampoline graph; ...

The gem graph is the fan graph F_(4,1) illustrated above. It is implemented in the Wolfram Language as GraphData["GemGraph"].

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...

The hexacode graph is the incidence graph of the unique symmetric transversal design STD_2[6;3]. It is also a bipartite (0,2)-graph. The hexacode graph is a ...