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The "contiguous USA graph" is the graph whose vertices represent the contiguous 48 states of the United States plus the District of Columbia (DC) and whose edges connect ...

A graph that is not finite is called infinite.

A n-crossed prism graph for positive even n (a term introduced here for the first time), is a graph obtained by taking two disjoint cycle graphs C_n and adding edges ...

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 ...

An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...

A biconnected graph is a connected graph having no articulation vertices (Skiena 1990, p. 175). An equivalent definition for graphs on more than two vertices is a graph G ...

A Hamiltonian graph, also called a Hamilton graph, is a graph possessing a Hamiltonian cycle. A graph that is not Hamiltonian is said to be nonhamiltonian. A Hamiltonian ...

A graph corresponding to the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, all of which are regular, planar, polyhedral, and Hamiltonian. The ...

A k-colored graph is a labeled k-colorable graph together with its coloring function (Finch 2003).

The E graph is the tree on 6 vertices illustrated above. It is isomorphic to the (3,2)-firecracker graph and 3-centipede graph. It is implemented in the Wolfram Language as ...