Extremal Polyomino Chains with Respect to General Sum-Connectivity Index

Abstract

For a (molecular) graph \(G\), the general sum-connectivity index \(\chi_\alpha(G)\) is defined as the sum of the weights \((d_u + d_v)^\alpha\) of all edges \(uv\) of \(G\), where \(d_u\) (or \(d_v\)) denotes the degree of a vertex \(u\) (or \(v\)) in \(G\) and \(\alpha\) is an arbitrary real number. In this paper, we give an efficient formula for computing the general sum-connectivity index of polyomino chains and characterize the extremal polyomino chains with respect to this index, which generalizes one of the main results in [Z. Yarahmadi, A. Ashrafi, S. Moradi, Extremal polyomino chains with respect to Zagreb indices, Appl. Math. Lett. 25 (2012): 166-171].