Remainder Cordial Labeling of Graphs

In this paper we introduce remainder cordial labeling of graphs. Let G be a (p; q) graph. Let f : V (G) ! f1; 2; :::; pg be a 1􀀀1 map. For each edge uv assign the label r where r is the remainder when f(u) is divided by f(v) or f(v) is divided by f(u) according as f(u) f(v) or f(v) f(u). The functionf is called a remainder cor- dial labeling of G if jef (0) 􀀀 ef (1)j 1 where ef (0) and ef (1) respectively denote the number of edges labeled with even integers and odd integers. A graph G with a remainder cordial labeling is called a remainder cordial graph. We investigate the remainder cordial behavior of path, cycle, star, bistar, crown, comb, wheel, complete bipartite K2;n graph. Finally we propose a conjecture on complete graph Kn.