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Trees with minimum weighted Szeged index

The Art of Discrete and Applied Mathematics
Summary: The weighted Szeged index is a recent extension of the well-known Szeged index. Trees are conjectured to achieve the minimum weighted Szeged index among all graphs with a given number of vertices. In this paper, we present new tools to analyze and characterize trees with minimum weighted Szeged index.
Pavol Hell   +2 more
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On revised Szeged index of a class of unicyclic graphs

Discrete Mathematics, Algorithms and Applications, 2021
Computing topological indices of graphs is a fundamental and classical topic. Let [Formula: see text] be a connected graph. The revised Szeged index [Formula: see text] is defined as [Formula: see text], where [Formula: see text] (respectively, [Formula: see text]) is the number of vertices whose distance to vertex [Formula: see text] (respectively ...
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On the difference between the (revised) Szeged index and the Wiener index of cacti

Discrete Applied Mathematics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sandi Klavzar   +2 more
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On the Revised Edge-Szeged Index of Graphs

2019
The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of edges of G lying closer to vertex v than to vertex u, and the number of edges ...
Liu, Hechao, You, Lihua, Tang, Zikai
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The Szeged Index and an Analogy with the Wiener Index

Journal of Chemical Information and Computer Sciences, 1995
Padmakar V. Khadikar   +5 more
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A note on revised Szeged index of graph operations

2018
Summary: Let \(G\) be a finite and simple graph with edge set \(E(G)\). The revised Szeged index is defined as \[ Sz^{\ast}(G)=\sum_{e=uv\in E(G)}(n_u(e| G)+\frac{n_{G}(e)}{2})(n_v(e| G)+\frac{n_{G}(e)}{2}), \] where \(n_u(e| G)\) denotes the number of vertices in \(G\) lying closer to \(u\) than to \(v\) and \(n_{G}(e)\) is the number of equidistant ...
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Szeged Index of Symmetric Graphs

Journal of Chemical Information and Computer Sciences, 1998
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Szeged Related Indices of TUAC6[p, q]

Journal of Discrete Mathematical Sciences and Cryptography, 2017
Wei Gao, Mohammad Reza Farahani
exaly  

Revised Szeged index and revised edge-szeged index of special chemical molecular structures

Journal of Interdisciplinary Mathematics, 2016
Wei Gao, Weifan Wang
exaly  

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