Root quad mean labeling for some special graphs

Abstract

A graph G $= (p,q)$ is a Root Quad Mean graph if there is an injective function f from the vertices of G to 1,2,…, $p^2 -1$ such that when each edge uv is labeled with $\frac{\sqrt{f(u)^4+f(v)^4}}{2}$ then the resultant edges are distinct. In this paper we proved Comb graph, Ladder graph , Slanting ladder graph, Gear graph, Helm graph and Heger graph are Root Quad Mean Graphs.