F-root square mean labeling of line graph of some graphs

Abstract

A function f is called a F-Root Square Mean labeling of a graph G(V,E) withp vertices and q edges if f: V(G) → {1,2,3,...,q + 1} is injective and the induced function f^∗defined as f^∗(uv) — [√f(u)²+f(v)²/2 for all uv ∈ E(G), is bijective. A graph that admits a F-Root Square Mean labeling is called a F-Root Square Mean graph. The line graph is one among the graph operations. In this paper, it is tried to analyse that the line graph operation preserves the F-Root Square Mean property. Here we have discussed the F-Root Square Meanness of line graph of the path, cycle, star, P_n°S₁, P_noS₂, [P_n; S₁], S(P_noS₁), ladder, slanting ladder, the crown graph C_no S₁and the arbitrary subdivision of S₃. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.