# On Extremal Graphs of Weighted Szeged Index

@article{Bok2019OnEG, title={On Extremal Graphs of Weighted Szeged Index}, author={Jan Bok and Boris Furtula and Nikola Jedli{\vc}kov{\'a} and Riste {\vS}krekovski}, journal={ArXiv}, year={2019}, volume={abs/1901.04764} }

An extension of the well-known Szeged index was introduced recently, named as weighted Szeged index ($\textrm{sz}(G)$). This paper is devoted to characterizing the extremal trees and graphs of this new topological invariant. In particular, we proved that the star is a tree having the maximal $\textrm{sz}(G)$. Finding a tree with the minimal $\textrm{sz}(G)$ is not an easy task to be done. Here, we present the minimal trees up to 25 vertices obtained by computer and describe the regularities…

## 7 Citations

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The weighted Szeged index and the weighted vertex-PI index of a connected graph $G$ are defined as $wSz(G) = \sum_{e=uv \in E(G)} (deg (u) + deg (v))n_u(e)n_v(e)$ and $wPI_v(G) = \sum_{e=uv \in E(G)}…

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