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

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.Publisher's Versio

Tadpole Domination in Graphs

A new type of the connected domination parameters called tadpole domination number of a graph is introduced. Tadpole domination number for some standard graphs is determined, and some bounds for this number are obtained. Additionally, a new graph, finite, simple, undirected and connected, is introduced named weaver graph. Tadpole domination is calculated for this graph with other families of graphs