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A member of a collection of sets is said to be maximal if it cannot be expanded to another member by addition of any element. Maximal sets are important in graph theory since ...

Given a collection of sets, a member set that is not a proper subset of another member set is called a minimal set. Minimal sets are important in graph theory, since many ...

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 size of a minimum edge cover in a graph G is known as the edge cover number of G, denoted rho(G). If a graph G has no isolated points, then nu(G)+rho(G)=|G|, where nu(G) ...

A search algorithm of a graph which explores all nodes adjacent to the current node before moving on. For cyclic graphs, care must be taken to make sure that no nodes are ...

The correspondence which relates the Hanoi graph to the isomorphic graph of the odd binomial coefficients in Pascal's triangle, where the adjacencies are determined by ...

Let a graph G=(V,E) be defined on vertex set V and edge set E. Then a construction sequence (or c-sequence) for G is a linear order on V union E in which each edge appears ...

A matching, also called an independent edge set, on a graph G is a set of edges of G such that no two sets share a vertex in common. It is not possible for a matching on a ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

The Kirchhoff index Kf, also simply called the resistance and denoted R (Lukovits et al. 1999), of a connected graph G on n nodes is defined by ...