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The (upper) vertex independence number of a graph, often called simply "the" independence number, is the cardinality of the largest independent vertex set, i.e., the size of ...

Iofinova and Ivanov (1985) showed that there exist exactly five bipartite cubic semisymmetric graphs whose automorphism groups preserves the bipartite parts and acts ...

The rectilinear crossing number of a graph G is the minimum number of crossings in a straight line embedding of G in a plane. It is variously denoted rcr(G), cr^_(G) ...

The term "snark" was first popularized by Gardner (1976) as a class of minimal cubic graphs with edge chromatic number 4 and certain connectivity requirements. (By Vizing's ...

The (lower) domination number gamma(G) of a graph G is the minimum size of a dominating set of vertices in G, i.e., the size of a minimum dominating set. This is equivalent ...

The Bellman-Ford algorithm is an algorithm for solving the shortest path problem, i.e., finding a graph geodesic between two given vertices. Other algorithms that can be used ...

A cube 9-compound can be constructed from the vertices of the first dodecahedron 2-compound. It will be implemented in a future version of the Wolfram Language as ...

A framework is called "just rigid" if it is rigid, but ceases to be so when any single bar is removed. Lamb (1928, pp. 93-94) proved that a necessary (but not sufficient) ...

A maximal independent set is an independent set which is a maximal set, i.e., an independent set that is not a subset of any other independent set. The generic term "maximal ...

A minimum clique covering is a clique covering of minimum size, and the size of such a minimum clique covering is known as the clique covering number. Note that while a ...