The irregularity of graphs under graph operations

摘要

The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑_(uv∈E(G)) |d_(G)(u) ? d_(G)(v)|, where d_(G)(u) denotes the degree of a vertex u ∈ V (G). In this paper we consider the irregularity of graphs under several graph operations including join, Cartesian product, direct product, strong product, corona product, lexicographic product, disjunction and sym- metric difference. We give exact expressions or (sharp) upper bounds on the irregularity of graphs under the above mentioned operations.