New Family of Parity Combination Cordial Labeling of Graph

Abstract

Let G be a (p, q) graph. Let f be an injective map from V(G) to {1, 2, …, p}. For each edge xy, assign the label         y x or         x y according as x > y or y > x. f is called a parity combination cordial labeling (PCC-labeling) if f is a one to one map and | ef(0) − ef(1) |  1 where ef(0) and ef(1) denote the number of edges labeled with an even number and odd number respectively. A graph with a parity combination cordial labeling is called a parity combination cordial graph (PCC-graph). In this paper we investigate the PCC- labeling of the graph G , It is obtained by identifying a vertex vk in G and a vertex of degree n in Hn, where G is a PCC graph with p vertices and q edges under f with f(vk) = 1.