Square Difference Prime Labeling for Duplication of Graphs
S. Alice Pappa1, G.J. Jeba Selvi Kavitha2

1Dr. S. Alice Pappa, Department of Mathematics, Nazareth Margoschis College, Pillaiyanmanai Tuticorin-Affiliated to Manonmaniam Sundaranar University Abishekapatti, Tirunelveli (Tamil Nadu), India.
2G.J. Jeba Selvi Kavitha, Research Scholar, Reg. No. 19232142092007, Department of Mathematics, Nazareth Margoschis College, Pillaiyanmanai Tuticorin – Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli (Tamil Nadu), India. and St. Joseph’s College of Arts and Science for Women – Hosur.
Manuscript received on 07 October 2022 | Revised Manuscript received on 15 October 2022 | Manuscript Accepted on 15 December 2022 | Manuscript published on 30 December 2022 | PP: 19-21 | Volume-12 Issue-2, December 2022 | Retrieval Number: 100.1/ijeat.B38671212222 | DOI: 10.35940/ijeat.B3867.1212222
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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
Keywords: Graph labelling, Graph labeling, Greatest Common Incidence Number (gcin), Square difference prime labelling (sqdp), Square difference Prime (SQDP)
Scope of the Article: Computer Graphics, Simulation, and Modelling