Toughness of Infinite Graphs

Kevin K.Ferland1
1Bloomsburg University, Bloomsburg, PA 17815

Abstract

We initiate a study of the toughness of infinite graphs by considering a natural generalization of that for finite graphs. After providing general calculation tools, computations are completed for several examples. Avenues for future study are presented, including existence problems for tough-sets and calculations of maximum possible toughness. Several open problems are posed.