Q8 difference cordial labeling

Abstract

Let Q8 be a quaternion group. Let G=(V,E) be a graph. Let f: V(G)→Q₈. For each edge xy assign the label 0 when |o(f(x))−o(f(y))|=0 and 1 otherwise. The function f is called Q₈ 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 Q₈ 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 Q₈ difference cordial labeling is called Q₈ 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 Q₈ cordial; cordial labeling; quaternion group labeling.