Edge Rupture Degree of Graphs.

The edge rupture degree of a graph , as one of measurement parameter of network vulnerability, is defined as , where is the number of components of and is the order of a largest component of . In this paper, general results on the edge-rupture degree of a graph are considered. Firstly, some bounds on edge rupture degree are given. Further, edge rupture degree of some graphs is caculated. Also some results are given about this parameter with others. Finally, we discuss edge rupture degree of the complement graph and give the Nordhaus-Gaddum-type results for edge rupture degree. [ABSTRACT FROM AUTHOR]