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A note on polyomino chains with extremum general sum-connectivity index | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 7، دوره 6، شماره 1، شهریور 2021، صفحه 81-91 اصل مقاله (412.15 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2020.26866.1153 | ||
| نویسندگان | ||
| Akbar Ali* 1؛ Tahir Idrees2 | ||
| 1University of Ha'il | ||
| 2University of Management and Technology, Sialkot, Pakistan | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| chemical graph theory؛ topological index؛ Randi'c index, general sum-connectivity index؛ polyomino chain | ||
| مراجع | ||
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