On Square Sum Labeling of Two Families of Petersen Graphs

Abstract

A labeling on a graph G with n vertices and m edges is called square sum if there exists a bijection f:VG⟶0,1,2,3,…,n−1 such that the function f∗:EG⟶N defined by f∗st=fs2+ft2, for all st∈EG, is injective. A graph G having a square sum labeling is called square sum. In this study, we have investigated the square sum labeling of generalized Petersen graph and double generalized Petersen graph.