Commun. Korean Math. Soc. 2022; 37(4): 969-975
Online first article May 13, 2022 Printed October 31, 2022
https://doi.org/10.4134/CKMS.c210348
Copyright © The Korean Mathematical Society.
Baha' Abughazaleh, Omar AbedRabbu Abughneim
Isra University; The University of Jordan
Let $R$ be a finite commutative ring with nonzero unity and let $Z(R)$ be the zero divisors of $R$. The total graph of $R$ is the graph whose vertices are the elements of $R$ and two distinct vertices $x,y\in R$ are adjacent if $x+y\in Z(R)$. The total graph of a ring $R$ is denoted by $\tau (R)$. The independence number of the graph $\tau (R)$ was found in \cite{Nazzal}. In this paper, we again find the independence number of $\tau (R)$ but in a different way. Also, we find the independent dominating number of $\tau (R)$ . Finally, we examine when the graph $\tau (R)$ is well-covered.
Keywords: Total graph of a commutative ring, zero divisors, independence number, independent dominating number, well-covered graphs
MSC numbers: 13M99, 05C69
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd