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AIMS Mathematics
Article . 2024 . Peer-reviewed
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AIMS Mathematics
Article . 2024
Data sources: DOAJ
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On the maximum atom-bond sum-connectivity index of unicyclic graphs with given diameter

Authors: Zhen Wang; Kai Zhou;

On the maximum atom-bond sum-connectivity index of unicyclic graphs with given diameter

Abstract

<p>Let $ G = (V(G), E(G)) $ be a simple connected graph with vertex set $ V(G) $ and edge set $ E(G) $. The atom-bond sum-connectivity (ABS) index was proposed recently and is defined as $ ABS(G) = \sum_{uv\in E(G)}\sqrt{\frac{d_{G}(u)+d_{G}(v)-2}{d_{G}(u)+d_{G}(v)}} $, where $ d_{G}(u) $ represents the degree of vertex $ u\in V(G) $. A connected graph $ G $ is called a unicyclic graph if $ |V(G)| = |E(G)| $. In this paper, we determine the maximum ABS index of unicyclic graphs with given diameter. In addition, the corresponding extremal graphs are characterized.</p>

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Keywords

atom-bond sum-connectivity index, pendent vertex, 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!
1
Average
Average
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