The connection degree index of graphs

The concept of Vulnerability is an important field of study of Graph Theory. Some measures of vulnerability Wiener Index, Degree Distance, Zagreb Index, Molecular Topologic Index, Eccentric Index have been developed in order to compare vulnerability of graphs. Degree distance concept is a measurement which consider the length of the shortest path between vertex pairs of graphs but the weakness of this measurement is ignoring the exceptions resulting from location of edges cannot be done comparison graph vulnerability efficiently at all the times. In this study we developed a new measurement for graph vulnerability which considers the special case of the location of the edges and some of the results of this measure feature and we applied this measure for some graphs.