Further results on Parity Combination Cordial Labeling
Abstract
Let G be a (p, q)-graph. Let f be an injective mapping from V(G) to {1, 2,…, p}. For each edge xy, assign the label ðxy Þ or ðyx Þ according as x > y or y > x. Call f a parity combination cordial labeling if |ef(0) − ef(1)| ≤ 1, where ef(0) and ef(1) denote the number of edges labeled with an even number and an odd number, respectively. In this paper we make a survey on all graphs of order at most six and find out whether they satisfy a parity combination cordial labeling or not and get an upper bound for the number of edges q of any graph to satisfy this condition and describe the parity combination cordial labeling for two families of graphs.
This paper has been withdrawn.