Let R be a commutative ring and I its proper ideal, let S(I) be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(

). It is the (undirected) graph with all elements of R as vertices, and for distinct x, y

R, the vertices x and y are adjacent if and only if x + y

S(I). The total graph of a commutative ring, that denoted by T(

), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y

Z(R) which is due to Anderson and Badawi [2]. In the case I = {0},

; this is an important result on the definition.