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A connected graph is said to be highly irregular if the neighbors of each vertex have distinct vertex degrees. Highly irregular graphs exist on all orders except 3, 5 and 7, ...

A quasi-qunitic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 ...

A double-toroidal graph is a graph with graph genus 2 (West 2000, p. 266). Planar and toroidal graphs are therefore not double-toroidal. Some known double-toroidal graphs on ...

A lobster graph, lobster tree, or simply "lobster," is a tree having the property that the removal of leaf nodes leaves a caterpillar graph (Gallian 2007). The numbers of ...

There exists no known P algorithm for graph isomorphism testing, although the problem has also not been shown to be NP-complete. In fact, the problem of identifying ...

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 ...