On product root sum mean labeling of some new class of graphs

Abstract

In 2019, a new labeling called Product Root Sum Mean Labeling was introduced in the literature . It is defined in a graph G=(p,q) as an injective function f: V →7{1,2,3,…,q+1} such that the induced function f* defined by f*(uv)=f(u)*f(v)+f(u)+f(v)2 yield different values on edges. A paper which admits this labeling is known as Product Root Sum Mean graph. In this paper we prove that the ladder graph , the Square Ladder graph , the cocunut tree CT(m,m), the graph Yr+1, the Star graph K1,n, the Shadow graph of Star K1,n , the Split graph of Star K1,n, the BiStar graph Kn,n, the Shadow graph of BiStar Kn,n, the Comb graph Pn⊙K1, the Square graph of Comb Pn⊙K1, the Shadow graph of Comb D2(Pn⊙K1) and the splitting graph of Comb are Product Root Sum Mean graphs.