%0 Journal Article %T A note on polyomino chains with extremum general sum-connectivity index %J Communications in Combinatorics and Optimization %I Azarbaijan Shahid Madani University %Z 2538-2128 %A Ali, Akbar %A Idrees, Tahir %D 2021 %\ 06/01/2021 %V 6 %N 1 %P 81-91 %! A note on polyomino chains with extremum general sum-connectivity index %K chemical graph theory %K topological index %K Randi'c index, general sum-connectivity index %K polyomino chain %R 10.22049/cco.2020.26866.1153 %X The general sum-connectivity index of a graph $G$ is defined as $\chi_{\alpha}(G)= \sum_{uv\in E(G)} (d_u + d_{v})^{\alpha}$ where $d_{u}$ is degree of the vertex $u\in V(G)$, $\alpha$ is a real number different from $0$ and $uv$ is the edge connecting the vertices $u,v$. In this note, the problem of characterizing the graphs having extremum $\chi_{\alpha}$ values from a certain collection of polyomino chain graphs is solved for $\alpha<0$. The obtained results together with already known results (concerning extremum $\chi_{\alpha}$ values of polyomino chain graphs) give the complete solution of the aforementioned problem. %U http://comb-opt.azaruniv.ac.ir/article_14100_a10c261c639facff76ab34a95c3f68f4.pdf