Cordial labelings of a Class of Planar Graphs

Abstract

Let G = (V, E) be a graph and let f: V → {0, 1} be a mapping from the set of vertices to {0, 1} and for each edge (u, v) ∊ E assign the label |f(u) — f(v)|. If the number of vertices labeled with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labled with 0 and the number of edges labeled with 1 differ by at most 1, then f is called a cordial labeling. In this paper, we present two families of planar graphs, Pln and Plm,n defined shortly, that admit a cordial labeling. We also show that the class Plm,n admits a total product cordial labeling under certain conditions.