Cohesion Stability Under Edge Destruction

In this paper, we examine the concept of cohesion, which was first introduced in \([2]\) and further studied in \([5]\). Our purpose is to consider the global effects on cohesion when an edge is deleted from a given graph. The earlier paper dealt with such effects when an edge was added, and then in a local sense. After some preliminary discussions and definitions, we move on to display graphs that are “nearly stable” under edge deletion and to further discover an infinite class of \(2\)-connected graphs that are indeed “stable”. This result is followed by some discussion of graphs that have more than one block.