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The Shi-Krotov-Solé graph is a weakly regular graph on 1024 vertices with regular parameters (nu,k,lambda,mu)=(1024,33,2,(0,2)). It is distance-regular but not ...

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 connected labeled graph with n graph edges in which all graph vertices can be labeled with distinct integers (mod n) so that the sums of the pairs of numbers at the ends of ...

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 3-coloring of graph edges so that no two edges of the same color meet at a graph vertex (Ball and Coxeter 1987, pp. 265-266).

A graph with graph edges of two possible "colors," usually identified as red and blue. For a bichromatic graph with R red graph edges and B blue graph edges, R+B>=2.

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 ...

For an undirected graph, an unordered pair of nodes that specify a line joining these two nodes are said to form an edge. For a directed graph, the edge is an ordered pair of ...

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

A Halin graph, sometimes known as a roofless polyhedron, is a polyhedral graph constructed from a planar embedding of a tree having four or more vertices, no vertices of ...