Some properties of total graphs

Let R be a commutative ring. The total graph of R, denoted by T($\gamma$(R)), is a graph with all elements of R as vertices, and two distinct vertices x, y $\in$ R are adjacent if and only if x + y $\in$ Z(R), where Z(R) denotes the set of zero-divisors of R. In this paper, we study the .((chromatic index, clique number and independence number of T($\gamma$(R