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The average disorder number of a simple connected graph on n vertices is defined as the average length of a walk along the edges of the graph taken over all ordering of its ...

In a graph G, contraction of an edge e with endpoints u,v is the replacement of u and v with a single vertex such that edges incident to the new vertex are the edges other ...

subjMathematics:Discrete Mathematics:Graph Theory:Cliques The maximal clique polynomial C_G(x) for the graph G may be defined as the polynomial ...

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 ...

Let A be an n×n matrix with complex or real elements with eigenvalues lambda_1, ..., lambda_n. Then the spectral radius rho(A) of A is rho(A)=max_(1<=i<=n)|lambda_i|, i.e., ...

The transitive closure of a binary relation R on a set X is the minimal transitive relation R^' on X that contains R. Thus aR^'b for any elements a and b of X provided that ...

A problem asking for the shortest tour of a graph which visits each edge at least once (Kwan 1962; Skiena 1990, p. 194). For an Eulerian graph, an Eulerian cycle is the ...

The set of all edge automorphisms of G, denoted Aut^*(G). Let L(G) be the line graph of a graph G. Then the edge automorphism group Aut^*(G) is isomorphic to Aut(L(G)), ...

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) ...