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arXiv · 1803.04657

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

Akbar Ali·Tahir Idrees
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Abstract

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 values of polyomino chain graphs) give the complete solution of the aforementioned problem.

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Akbar Ali, Tahir Idrees. 2018-03-13. A note on polyomino chains with extremum general sum-connectivity index. https://arxiv.org/abs/1803.04657

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