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Title:
On General Sum-Connectivity Index of Trees of Fixed Maximum Degree and Order
Authors:
Zahid Raza, Selvaraj Balachandran, Suresh Elumalai, Akbar Ali
doi:
Volume
88
Issue
3
Year
2022
Pages
643-658
Abstract The general sum-connectivity index is a molecular descriptor introduced within the field of mathematical chemistry about a decade ago. For an arbitrary real number \(\alpha\), the general sum-connectivity index of a graph \(G\) is denoted \(\chi_{\alpha}(G)\) and is defined as the sum of the numbers \(\left(d(u) + d(v)\right)^{\alpha}\) over all edges \(uv\) of \(G\), where \(d(u)\) and \(d(v)\) denote the degrees of the vertices \(u\) and \(v\), respectively. This paper characterizes the trees attaining the extremum values of \(\chi_{\alpha}\) over the class of all trees of order \(n\) and maximum degree \(\Delta\) for \(\alpha <0\) as well as for \(\alpha>1\), where \(3 \leq \left\lceil n/2\right\rceil \leq \Delta \leq n-2\).

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