• MEAN SQUARE SUM LABELING OF PATH RELATED GRAPHS

Abstract

Let G = (V, E) be a graph. A bijection f: →{0, 1, ..., p-1}  is said to be a mean square sum labeling if the induced function f*:E(G)→N given by f*(uv) =  or  for every uv ∈  is injective. A graph which admits a mean square sum labeling is called a mean square sum graph. The concept of mean square sum labeling was introduced by C. Jayasekaran, S. Robinson Chellathurai and M. Jaslin Melbha and they investigated the mean square sum labeling of several standard graphs and some cycle related graphs. In this paper, we prove that composition of paths P_m and P₂, , , D₂(P_n), Splitting graph of path P_n, Switching of a pendant vertex in path P_n, T_n, DT_n, Coconut tree and the graph obtained from P_n by attaching C₃ in both the end edges of P_n are mean square sum graph.