Lower Domination Polynomial of a Graph

Abstract

In literature, we find many topological indices based on the degree of the vertex. In this article, we initiate the study of a new index which takes into account, the smallest dominating set involving a vertex. This is called as lower domination number of a graph relative to a vertex. Using this lower domination number of a graph relative to a vertex, we have introduced new indices called Lower Domination Index and Lower Domination coindex of a graph. We have obtained the relation between these indices and co-indices for a general graph and these indices have been obtained for different graphs and their derived graphs. A new graph polynomial called Lower Domination Polynomial has been introduced and is obtained for some standard graphs.