Estimating the connectivity of a graph

Abstract

Although the results above seem to yield good estimators of an upper bound on connectivity, they can easily give rather poor estimates of k itself. One possible improvement could be effected by using the theorem of Harary and Chartrand [2] that δ≥p−2+n / 2 for some n such that 1≤n≤p−1 implies k≧n. This could give an estimate of a lower bound on k by using δ* in place of δ in the above inequality. Of course, the usefulness of this is limited to cases in which δ* is rather large, at least 1/2 p. Further approaches to this problem based on testing the hypothesis that k=1 will hopefully be the subject of a future paper.