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Sharp bounds for the general sum-connectivity indices of transformation graphs. (English) Zbl 1401.05160
Summary: Given a graph \(G\), the general sum-connectivity index is defined as \(\chi_\alpha(G) = \sum_{u v \in E(G)} \left(d_G \left(u\right) + d_G \left(v\right)\right)^\alpha\), where \(d_G(u)\) (or \(d_G(v)\)) denotes the degree of vertex \(u\) (or \(v\)) in the graph \(G\) and \(\alpha\) is a real number. In this paper, we obtain the sharp bounds for general sum-connectivity indices of several graph transformations, including the semitotal-point graph, semitotal-line graph, total graph, and eight distinct transformation graphs \(G^{u v w}\), where \(u, v, w \in \left\{+, -\right\}\).

05C35 Extremal problems in graph theory
Full Text: DOI
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