Changing and unchanging on Tadpole domination number in G − e, G + e graphs

Abstract

In this paper, the effect of “Tadpole domination” change is examined, which is one of the domination types, when a graph is modified, by deleting or adding an edge in G. This edge deletion may represent a cut in a network. The occurrence of any interruption in connections of this network may lead to the pause of data transmission in the network and thus affect the work of the entire network, as well as the need to create new necessary connections within the network or excluding others for the possibility of reducing the cost. Based on these criteria “Tadpole domination number” change has been examined. The increase, decrease, and non-increase or decrease was determined for this number, in case of deletion or addition, and we have proved some basic cases for this domination change.