On the Line Graph for Zero-Divisors of C(X). (31st December 2013) - AlAfifi, Ghada; Abu Osba, Emad
Abstract : Let beX a completely regular Hausdorff space and letC ( X ) be the ring of all continuous real valued functions defined onX . In this paper, the line graph for the zero-divisor graph ofC ( 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 ifX 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 ofX .