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A k-regular simple graph G on nu nodes is strongly k-regular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a ...

The (weak) Bruhat graph B_n of order n is the simple graph having have all permutations of {1,2,...,n} as vertices, and with an edge between pairs of permutations that differ ...

The word "rigid" has two different meaning when applied to a graph. Firstly, a rigid graph may refer to a graph having a graph automorphism group containing a single element. ...

The skeleton graphs of the Johnson solids are polyhedral graphs. The Johnson skeleton graphs J_3 and J_(63) are minimal unit-distance forbidden graphs. The skeleton of the ...

Let G be a graph and S a subgraph of G. Let the number of odd components in G-S be denoted S^', and |S| the number of graph vertices of S. The condition |S|>=S^' for every ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

A cactus graph, sometimes also called a cactus tree, a mixed Husimi tree, or a polygonal cactus with bridges, is a connected graph in which any two graph cycles have no edge ...

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 graph G is distance transitive if its automorphism group is transitive on pairs of vertices at each pairwise distance in the graph. Distance-transitivity is a ...

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