3-Difference Cordiality of Some Special Graphs

Abstract

Let G bea(p,q) graph. Let f : V(G) → {1,2,...,k} be a map where k is an integer 2 ≤ k ≤ p. For each edge uv, assign the label |f(u) −f(v)|. f is called k-difference cordial labeling of G if |v_f(i) − v_f(j)| ≤ 1 and |e_f(0) − e_f(1)| ≤ 1 where v_f(x) denotes the number of vertices labelled with x, e_f(1) and e_f(0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a  k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate 3-difference cordial labeling behavior of ladder, book, dumbbell graph, and umbrella graph.

Key words and phrases. Path, ladder, book, dumbbell graph, umbrella graph.

2000 Mathematics Subject Classification. 05C78