Q8 difference cordial labeling

Abstract

Let Q8 be a quaternion group. Let G=(V,E) be a graph. Let f: V(G)→Q 8 . For each edge xy assign the label 0 when |o(f(x))−o(f(y))|=0 and 1 otherwise. The function f is called Q 8 cordial difference labeling of G if |v f (x)−v f (y)|≤1 and |e f (0)−e f (1)|≤1, where v f (x), v f (y) denote the total number of vertices labeled with x, y in Q 8 and e f (0), e f (1) denote the total number of edges labeled with 0,1 respectively. A graph G which admits a group Q 8 difference cordial labeling is called Q 8 difference cordial graph. In this paper, we prove the existence of this labeling to the graphs viz., path, ladder related graphs and snake related graphs. Keywords: group Q 8 cordial; cordial labeling; quaternion group labeling.