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Mathematics
Article . 2021 . Peer-reviewed
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Mathematics
Article
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Mathematics
Article . 2021
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On the Paired-Domination Subdivision Number of Trees

Authors: Shouliu Wei; Guoliang Hao; Seyed Mahmoud Sheikholeslami; Rana Khoeilar; Hossein Karami;

On the Paired-Domination Subdivision Number of Trees

Abstract

A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number γpr(G) of G. The paired-domination subdivision number sdγpr(G) of G is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the paired-domination number. Here, we show that, for each tree T ≠ P5 of order n ≥ 3 and each edge e ∉ E(T), sdγpr(T) + sdγpr(T + e) ≤ n + 2.

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Keywords

QA1-939, paired-domination subdivision number, paired-domination number, 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
Average
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