Parity Combination Cordial Labeling of Graphs

Abstract

In this paper we define a new graph labeling called parity combination cordial labeling. 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 (^x_y) or (^y_x) 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 | e_f (0) - e_f (1) | ≤ 1 where e_f (0) and e_f (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). Also we investigate the PCC-labeling behavior of path, cycle, fan, comb, complete graph, wheel, crown, star. A conjecture is stated at the end.

Key words and phrases. path, cycle, comb, star, wheel.

1991 Mathematics Subject Classification. 05C78