NDLI: On the Paired-Domination Subdivision Number of a Graph

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On the Paired-Domination Subdivision Number of a Graph

Content Provider	MDPI
Author	Hao, Guoliang Sheikholeslami, Seyed Chellali, Mustapha Khoeilar, Rana Karami, Hossein
Copyright Year	2021
Abstract	In order to increase the paired-domination number of a graph G, the minimum number of edges that must be subdivided (where each edge in G can be subdivided no more than once) is called the paired-domination subdivision number ${sd}_{γ_{p r}} (G)$ of G. It is well known that ${sd}_{γ_{p r}} (G + e)$ can be smaller or larger than ${sd}_{γ_{p r}} (G)$ for some edge $e \notin E (G) .$ In this note, we show that, if G is an isolated-free graph different from $m K_{2},$ then, for every edge $e \notin E (G)$ , ${sd}_{γ_{p r}} (G + e) \leq {sd}_{γ_{p r}} (G) + 2 Δ (G)$ .
Starting Page	439
e-ISSN	22277390
DOI	10.3390/math9040439
Journal	Mathematics
Issue Number	4
Volume Number	9
Language	English
Publisher	MDPI
Publisher Date	2021-02-23
Access Restriction	Open
Subject Keyword	Mathematics Logic Paired-domination Number Paired-domination Subdivision Number
Content Type	Text
Resource Type	Article

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