Secure monophonic domination of graphs
Let G = (V, E) be a connected graph. A monophonic dominating set M is said to be a secure monophonic dominating set Sm (abbreviated as SMD set) of G if for each v∈V \M there exists u∈M such that v is adjacent to u and Sm = {M \(u)} ∪{v} is a monophonic dominating set. The minimum cardinality of a se...
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University of Mohaghegh Ardabili
2024-12-01
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| Series: | Journal of Hyperstructures |
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| Online Access: | https://jhs.uma.ac.ir/article_3547_cbbf01bc4e292c3dd405e680fd1a9eb6.pdf |
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| author | K Sunitha D Divya |
| author_facet | K Sunitha D Divya |
| author_sort | K Sunitha |
| collection | DOAJ |
| description | Let G = (V, E) be a connected graph. A monophonic dominating set M is said to be a secure monophonic dominating set Sm (abbreviated as SMD set) of G if for each v∈V \M there exists u∈M such that v is adjacent to u and Sm = {M \(u)} ∪{v} is a monophonic dominating set. The minimum cardinality of a secure monophonic dominating set of G is the secure monophonic domination number of G and is denoted by γsm(G). In this paper, we investigate the secure monophonic domination number of subdivision of graphs such as subdivision of Path graph S(Pn), subdivision of Cycle graph S(Cn), subdivision of Star graph S(K1,n-1), subdivision Bistar graph S(Bm,n) and subdivision of Y-tree graph S(Yn+1). |
| format | Article |
| id | doaj-art-4b8b972127474df59a0182b52260bd2f |
| institution | OA Journals |
| issn | 2251-8436 2322-1666 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | University of Mohaghegh Ardabili |
| record_format | Article |
| series | Journal of Hyperstructures |
| spelling | doaj-art-4b8b972127474df59a0182b52260bd2f2025-08-20T02:36:16ZengUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-84362322-16662024-12-0113224725610.22098/jhs.2024.16053.10573547Secure monophonic domination of graphsK Sunitha0D Divya1Department of Mathematics, Scott Christian College(Autonomous), Nagercoil, IndiaDevasahayam Mount, AralvaimozhiLet G = (V, E) be a connected graph. A monophonic dominating set M is said to be a secure monophonic dominating set Sm (abbreviated as SMD set) of G if for each v∈V \M there exists u∈M such that v is adjacent to u and Sm = {M \(u)} ∪{v} is a monophonic dominating set. The minimum cardinality of a secure monophonic dominating set of G is the secure monophonic domination number of G and is denoted by γsm(G). In this paper, we investigate the secure monophonic domination number of subdivision of graphs such as subdivision of Path graph S(Pn), subdivision of Cycle graph S(Cn), subdivision of Star graph S(K1,n-1), subdivision Bistar graph S(Bm,n) and subdivision of Y-tree graph S(Yn+1).https://jhs.uma.ac.ir/article_3547_cbbf01bc4e292c3dd405e680fd1a9eb6.pdfmonophonic pathmonophonic domination numbersecure mono- phonic domination number |
| spellingShingle | K Sunitha D Divya Secure monophonic domination of graphs Journal of Hyperstructures monophonic path monophonic domination number secure mono- phonic domination number |
| title | Secure monophonic domination of graphs |
| title_full | Secure monophonic domination of graphs |
| title_fullStr | Secure monophonic domination of graphs |
| title_full_unstemmed | Secure monophonic domination of graphs |
| title_short | Secure monophonic domination of graphs |
| title_sort | secure monophonic domination of graphs |
| topic | monophonic path monophonic domination number secure mono- phonic domination number |
| url | https://jhs.uma.ac.ir/article_3547_cbbf01bc4e292c3dd405e680fd1a9eb6.pdf |
| work_keys_str_mv | AT ksunitha securemonophonicdominationofgraphs AT ddivya securemonophonicdominationofgraphs |