A note on polyomino chains with extremum general sum-connectivity index

Ali, Akbar; Idrees, Tahir

doi:10.22049/cco.2020.26866.1153

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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&#039;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

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A note on polyomino chains with extremum general sum-connectivity index