The sharp bounds on general sum-connectivity index of four operations on graphs

Abstract

The general sum-connectivity index χα( G) , for a (molecular) graph G, is defined as the sum of the weights (dG(a1)+dG(a2))α of all a1a2∈ E( G) , where dG( a1) (or dG( a2) ) denotes the degree of a vertex a1 (or a2) in the graph G; E( G) denotes the set of edges of G, and α is an arbitrary real number. Eliasi and Taeri (Discrete Appl. Math. 157:794-803, 2009) introduced four new operations based on the graphs S( G) , R( G) , Q( G) , and T( G) , and they also computed the Wiener index of these graph operations in terms of W( F( G) ) and W( H) , where F is one of the symbols S, R, Q, T. The aim of this paper is to obtain sharp bounds on the general sum-connectivity index of the four operations on graphs.