Parity combination cordial labeling of graphs

Abstract EN

In this paper we de ne 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 f1; 2; : : : ; pg.

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 jef (0) ? ef (1)j 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).

Also we investigate the PCC-labeling behavior of path, cycle, fan, comb, complete graph, wheel, crown, star.

A conjecture is stated at the