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The Harries-Wong graph is one of the three (3,10)-cage graphs, the other two being the (10,3)-cage known as the Balaban 10-cage and the Harries graph. The Harries-Wong graph ...

The 13 Archimedean dual graphs are the skeletons of the Archimedean dual solids, illustrated above. Since they are polyhedral graphs, they are also planar. However, none of ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

The dodecadodecahedral graph is the skeleton of the dodecadodecahedron, great dodecahemicosahedron, and small dodecahemicosahedron. It is illustrated above in several ...

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

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

The Cartesian graph product G=G_1 square G_2, also called the graph box product and sometimes simply known as "the" graph product (Beineke and Wilson 2004, p. 104) and ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

A 1-factor of a graph G with n graph vertices is a set of n/2 separate graph edges which collectively contain all n of the graph vertices of G among their endpoints.

A random graph is a graph in which properties such as the number of graph vertices, graph edges, and connections between them are determined in some random way. The graphs ...