On the Line Graph for Zero-Divisors of C(X)‎

الملخص EN

Let be X a completely regular Hausdorff space and let C(X) be the ring of all continuous real valued functions defined on X.

In this paper, the line graph for the zero-divisor graph of C(X) is studied.

It is shown that this graph is connected with diameter less than or equal to 3 and girth 3.

It is shown that this graph is always triangulated and hypertriangulated.

It is characterized when the graph is complemented.

It is proved that the radius of this graph is 2 if and only if X has isolated points; otherwise, the radius is 3.

Bounds for the dominating number and clique number are also found in terms of the density number of X.