For a graph G and k a real number, we consider the sum of the k-th powers of the degrees of the vertices of G. We present some general bounds on this sum for various values of k. ...
We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP...
Michal Malafiejski, Krzysztof Giaro, Robert Jancze...
A graph of order n is said to be pancyclic if it contains cycles of all lengths from three to n. Let G be a hamiltonian graph and let x and y be vertices of G that are consecutive ...
Michael Ferrara, Michael S. Jacobson, Angela Harri...
We give a basis for the space spanned by the sum ^s of the lowest degree terms in the expansion of the Schur symmetric functions s in terms of the power sum
A weighted graph is one in which every edge e is assigned a nonnegative number w(e), called the weight of e. The weight of a cycle is defined as the sum of the weights of its edge...