The cordiality of the path-union of n copies of a graph

Abstract

Let G1, G2,..., Gn be n (≥2) copies of a graph G. We denote by G (n) the graph obtained by adding an edge to Gi and Gi+1, i = 1, 2,..., n - 1, and we call G(n) the path-union of n copies of the graph G. We shall relate the cordiality of the path-union of n copies of a graph to the solution of a system involving an equation and two inequalities, and give some sufficient conditions for that path-union to be cordial. The path-unions of such graphs as cycles, wheels, fans, some cliques, Cartesian products and compositions of some graphs are shown to be cordial.