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For a connected bipartite graph G, the halved graph G^+ and G^- are the two connected components of the distance 2-graph of G. The following table summarizes some named ...

The Hochberg-O'Donnell fish graph is the unit-distance graph on 23 nodes and 42 edges illustrated above. It is triangle-free and is the smallest example of a unit-distance ...

A graph G is fully reconstructible in C^d if the graph is determined from its d-dimensional measurement variety. If G is globally rigid in R^d on n>=d+2 vertices, then G is ...

A weakly perfect graph is a graph for which omega(G)=chi(G) (without any requirement that this condition also hold on induced subgraphs, which is required for a graph to be ...

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 likelihood of a simple graph is defined by starting with the set S_1={(K_11)}. The following procedure is then iterated to produce a set of graphs G_n of order n. At step ...

A directed strongly regular graph is a simple directed graph with adjacency matrix A such that the span of A, the identity matrix I, and the unit matrix J is closed under ...

A k×m×n hexagonal grid graph is a graph of adjoined hexagons consisting of k hexagons along the horizontal triangular axis, m along the northeast axis, and n along the ...

A generalized Moore graph is a regular graph of degree r where the counts of vertices at each distance d=0, 1, ... from any vertex are 1, r, r(r-1), r(r-1)^2, r(r-1)^3, ..., ...

The ditrigonal icosidodecahedral graph is the skeleton of the cube 5-compound, ditrigonal dodecadodecahedron, great ditrigonalIcosidodecahedron, and small ditrigonal ...