The independence and independent dominating numbers of the total graph of a finite commutative ring

11.Oct.2022

Let  be a finite commutative ring with nonzero unity and let �(�) be the zero divisors of . The total graph of  is the graph whose vertices are the elements of  and two distinct vertices �,�∈� are adjacent if �+�∈�(�). The total graph of a ring  is denoted by �(�). The independence number of the graph �(�) was found in \cite{Nazzal}. In this paper, we again find the independence number of �(�) but in a different way. Also, we find the independent dominating number of �(�) . Finally, we examine when the graph �(�) is well-covered.