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. |
Jñānābha > Volume 50 (No 1-2020) >