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Weighted Szeged index is a recently introduced extension of the well-known Szeged index. In this paper, we present a new tool to analyze and characterize minimum weighted Szeged index trees. We exhibit the best trees with up to 81 vertices and use this information, together with our results, to propose various conjectures on the structure of minimum weighted Szeged index trees.
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 t
The edge Szeged index and edge-vertex Szeged index of a graph are defined as $Sz_{e}(G)=sumlimits_{uvin E(G)}m_{u}(uv|G)m_{v}(uv|G)$ and $Sz_{ev}(G)=frac{1}{2} sumlimits_{uv in E(G)}[n_{u}(uv|G)m_{v}(uv|G)+n_{v}(uv|G)m_{u}(uv|G)],$ respectively, wher
The edge Szeged index of a graph $G$ is defined as $Sz_{e}(G)=sumlimits_{uvin E(G)}m_{u}(uv|G)m_{v}(uv|G)$, where $m_{u}(uv|G)$ (resp., $m_{v}(uv|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the distance to ve
Let $Sz(G),Sz^*(G)$ and $W(G)$ be the Szeged index, revised Szeged index and Wiener index of a graph $G.$ In this paper, the graphs with the fourth, fifth, sixth and seventh largest Wiener indices among all unicyclic graphs of order $ngeqslant 10$ ar
Let $G$ be a connected graph. The edge revised Szeged index of $G$ is defined as $Sz^{ast}_{e}(G)=sumlimits_{e=uvin E(G)}(m_{u}(e|G)+frac{m_{0}(e|G)}{2})(m_{v}(e|G)+frac{m_{0}(e|G)}{2})$, where $m_{u}(e|G)$ (resp., $m_{v}(e|G)$) is the number of edge