Domination and Total Domination Contraction Numbers of Graphs

Abstract

In this paper, we consider the effect of edge contraction on the domination number and total domination number of a graph. We define the (total) domination contraction number of a graph as the minimum number of edges that must be contracted in order to decrease the (total) domination number. We show that both of these two numbers are at most three for any graph. In view of this result, we classify graphs by their (total) domination contraction numbers and characterize these classes of graphs.