Square Difference Prime Labeling for Duplication of Graphs

Abstract

Let G(V, E) be a graph with pvertices and qedges. Let f∶ V (G) → {0,1,2,…, p-1} be a bijection such that the induced function f*: E(G) → N defined by f_sqdp* (uv)=|[f(u) ]2-[f(v) ]2 | for everyuv∈E(G).If f_sqdp* is injective, then f_sqdp*is calledsquare difference labeling of G.A graph Gwhich admits square difference labeling is called square difference graph. The greatest common incidence number (gcin) of a vertex v of degree v > 1 is defined as the greatest common divisor (g.c.d) of the labels of the incident edges on v. A square difference labeling fis said to be a square difference prime labeling if for each vertex v of degree >1 then gcin(v) = 1. In this paper we investigate the square difference prime labelling of Petal graph and duplication of petal graph