Cohesion Stability Under Edge Destruction

Abstract

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.