Extremal polyomino chains with respect to general Randić index

Abstract

For a (molecular) graph $G,$ the general Randić index $R_{\alpha }(G)$ 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 Randić index of polyomino chains and characterize the extremal polyomino chains with respect to this index, which generalizes one of the main results in (Yarahmadi et al. Appl Math Lett 25:166–171, 2012).