Forgotten Index of duplication and double duplication of graphs by means of degree sequences

Abstract

The concept of forgotten index of a graph G was introduced by Furtula and Gutman in 2015 as F(G) = Σu∈v(G) d3uwhere duis the degree of a vertex u in G. It is a degree based topological index that correlates well with many physio-chemical properties of organic compounds. Duplication of a vertex by an edge and duplication of an edge by a vertex of graphs were introduced by Vaidya et al. in 2009. Double duplication of graphs were introduced by Shobana and Roopa in 2017. In this paper, some general results and inequalities on forgotten index of duplication and double duplication of graphs using degree sequence and edge and vertex partitions of these duplication graphs are obtained.