COMPLEMENT GRAPHS FOR ZERO - DIVISORS OF C(X)

Let X be a completely regular Hausdorff space and let C(X) be the ring of all continuous real valued functions defined on X. The complement graph for the zero-divisors in C(X) is a simple graph in which two zero-divisor functions are adjacent if their product is non-zero. In this article, the complement graph for the zero-divisor graph of C(X) and its line graph are studied. It is shown that if X has more than 2 points, then these graphs are connected with radius 2, and diameter less than or equal to 3. The girth is also calculated for them to be 3, and it is shown that they are always triangulated and hypertriangulated. Bounds for the dominating number and clique number are also found for them in terms of the density number of X.