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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 $$u, v, w \in \left\{+, -\right\}$$.

##### MSC:
 05C35 Extremal problems in graph theory
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