3−Remainder Cordial Labeling of Cycle Related Graphs

Abstract

Let G be a (p, q) graph. Let f be a function from V (G) to the set {1, 2, . . . , k} where k is an integer 2 < k ≤ |V (G)|. 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). Then the function f is called a k-remainder cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, . . . , k} where vf (x) denote the number of vertices labeled with x and |ηe – ηo| ≤ 1 where ηe and ηo respectively denote the number of edges labeled with an even integers and number of edges labeled with an odd integers. A graph admits a k-remainder cordial labeling is called a k- remainder cordial graph. In this paper we investigate the 3- remainder cordial labeling behavior of the Web graph, Umbrella graph, Dragon graph, Butterfly graph, etc.