THE INDEPENDENCE AND INDEPENDENT DOMINATING NUMBERS OF THE TOTAL GRAPH OF A FINITE COMMUTATIVE RING

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 epsilon R are adjacent if x broken vertical bar y epsilon 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 [11]. 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.