Computing Bounds for Second Zagreb Coindex of Sum Graphs

Abstract

Topological indices or coindices are one of the graph-theoretic tools which are widely used to study the different structural and chemical properties of the under study networks or graphs in the subject of computer science and chemistry, respectively. For these investigations, the operations of graphs always played an important role for the study of the complex networks under the various topological indices or coindices. In this paper, we determine bounds for the second Zagreb coindex of a well-known family of graphs called $F$ -sum ( $S$ -sum, $R$ -sum, $Q$ -sum, and $T$ -sum) graphs in the form of Zagreb indices and coindices of their factor graphs, where these graphs are obtained by using four subdivision-related operations and Cartesian product of graphs. At the end, we illustrate the obtained results by providing the exact and bonded values of some specific $F$ -sum graphs.