Group mean cordial labeling of some path and cycle related graphs

Abstract

Let G be a (p,q) graph and let A be a group. Let f: V(G)->A be a map. For each edge uv assign the label [o(f(u))+o(f(v))/2]. Here o(f(u)) denotes the order of f(u) as an element of the group A. Let I be the set of all integers that are labels of the edges of G. f is called a group mean cordial labeling if the following conditions hold:

(1) For x,y∈A, |v_f(x)−v_f(y)|≤1, where v_f(x) is the number of vertices labeled with x.

(2) For i,j∈I, |e_f(i)−e_f(j)|≤1, where e_f(i) denote the number of edges labeled with i.

A graph with a group mean cordial labeling is called a group mean cordial graph. In this paper, we take A as the group of fourth roots of unity and prove that, the graphs Ladder, Slanting Ladder, Triangular Ladder, Fan, Flower and Sunflower are group mean cordial graphs.