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The cyclotomic graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a cube in the finite field GF(q). This graph is ...

A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...

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 ...

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 white bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board), when ...

The Jørgensen graph is a maximally linklessly embeddable graph on 8 vertices and 21 edges, where "maximal" means it is not a proper subgraph of another linklessly embeddable ...

The smallest possible number of vertices a polyhedral nonhamiltonian graph can have is 11, and there exist 74 such graphs. The Goldner-Harary graph (Goldner and Harary 1975a, ...

A planar hypotraceable graph is a hypotraceable graph that is also planar. A number of planar hypotraceable graphs are illustrated above. Using a theorem of Thomassen (1974), ...

A fiveleaper graph is a graph formed by all possible moves of a hypothetical chess piece called a "fiveleaper" which moves analogously to a knight except that it is ...

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 ...