Jñānābha‎, Vol. 50 (1) (2020), 14-19

ENERGY OF SOME GRAPHS OF PRIME GRAPH OF A RING

By

Sandeep S. Joshi

Department of Mathematics,

D.N.C.V.P’s Shirish Madhukarrao Chaudhari College,

Jalgaon - 425 001, Maharashtra, India

sandeep.s.joshi07@gmail.com

Kishor F. Pawar

Department of Mathematics, School of Mathematical Sciences,

Kavayitri Bahinabai Chaudhari North Maharashtra University,

Jalgaon - 425 001, Maharashtra, India

kfpawar@nmu.ac.in

(Received : September 10, 2019 ; Revised: March 04, 2020)

Abstract

Let R be a commutative ring and PG(R) is a graph whose vertices are all the elements of ring R and two vertices are adjacent if their product is zero. In this article, we study the energy of 1-Quasitotal and 2-Quasitotal Prime Graph of a Ring Zp and also find the energy of PG 1 (Zp ) and PG 2 (Zp ), p prime. A General SCILAB Software code for our calculation is also presented.

2010 Mathematics Subject Classifications: 05C25, 05C15, 13E15.

Keywords and phrases: Ring, Prime graph of a Ring PG(R), Quasi-total graph, Energy.

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