Group mean cordial labeling of some path and cycle related graphs

R.N. Rajalekshmi, R. Kala

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, |vf(x)−vf(y)|≤1, where vf(x) is the number of vertices labeled with x.

(2) For i,j∈I, |ef(i)−ef(j)|≤1, where ef(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.

Full Text: PDF

Published: 2022-07-04

How to Cite this Article:

R.N. Rajalekshmi, R. Kala, Group mean cordial labeling of some path and cycle related graphs, J. Math. Comput. Sci., 12 (2022), Article ID 183

Copyright © 2022 R.N. Rajalekshmi, R. Kala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

Copyright ©2022 JMCS