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AIMS Mathematics
Article . 2023 . Peer-reviewed
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AIMS Mathematics
Article . 2023
Data sources: DOAJ
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The extremal unicyclic graphs with given diameter and minimum edge revised Szeged index

Authors: Shengjie He; Qiaozhi Geng; Rong-Xia Hao;

The extremal unicyclic graphs with given diameter and minimum edge revised Szeged index

Abstract

<abstract><p>Let $ H $ be a connected graph. The edge revised Szeged index of $ H $ is defined as $ Sz^{\ast}_{e}(H) = \sum\limits_{e = uv\in E_H}(m_{u}(e|H)+\frac{m_{0}(e|H)}{2})(m_{v}(e|H)+\frac{m_{0}(e|H)}{2}) $, where $ m_{u}(e|H) $ (resp., $ m_{v}(e|H) $) is the number of edges whose distance to vertex $ u $ (resp., $ v $) is smaller than to vertex $ v $ (resp., $ u $), and $ m_{0}(e|H) $ is the number of edges equidistant from $ u $ and $ v $. In this paper, the extremal unicyclic graphs with given diameter and minimum edge revised Szeged index are characterized.</p></abstract>

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Keywords

edge revised szeged index, edge szeged index, QA1-939, diameter, unicyclic graph, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
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