Square Sum And Square Difference Labelings Of Semitotal-block Graph For Some Class Of Graphs

Abstract

A graph G is said to be square sum and square difference labeling, if there exists a bijection f from V (G) to {1, 2, 3, ..., (p − 1)} which induces the injective function f ∗ from E(G) to N, defined by f ∗(uv) = f(u)2 + f(v)2 and f ∗(uv) = f(u)2 − f(v)2 respectively, for each uv ∈ E(G) and the resulting edges are distinctly labeled. G is said to be square sum and square difference graph, if it asdmits a square sum and square difference labeling respectively. The present work investigates, square sum and square difference labeling of semitotal-block graph for some class of graphs which are proved using number theory concept.

Keywords

• square sum labeling (ssl), square difference labeling( sdl) , semitotal-block graph, comb graph, crown graph, and friendship graph.