On graphs with graphic imbalance sequences

Abstract

The imbalance of the edge e = uv in a graph G is the value imbG(e) = |dG(u) − dG(v)|. We prove that the sequence MG of all edge imbalances in G is graphic for several classes of graphs including trees, graphs in which all non-leaf vertices form a clique and the so-called complete extensions of paths, cycles and complete graphs. Also, we formulate two interesting conjectures related to graphicality of MG.