On the monophonic global domination number of a graph
UDC 519.17 We introduce the monophonic global domination number $\overline{\gamma}_m(G)$ by combining monophonic convexity (via chordless paths) with the global domination in a graph and its complement. A monophonic global dominating set is defined, and $\overline{\gamma}_m(G)$ is regarded as the mi...
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| Date: | 2026 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7618 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1866663706383876096 |
|---|---|
| author | Selvi, V. John, J. Flower, V. Sujin Selvi, V. John, J. Flower, V. Sujin |
| author_facet | Selvi, V. John, J. Flower, V. Sujin Selvi, V. John, J. Flower, V. Sujin |
| author_institution_txt_mv | [
{
"author": "V. Selvi",
"institution": "PG and Research Department of Mathematics, M. V. Muthiah Government Arts College for Women, Dindigul, India"
},
{
"author": "J. John",
"institution": "Department of Mathematics, Government College of Engineering, Tirunelveli, India"
},
{
"author": "V. Sujin Flower",
"institution": "Department of Mathematics, Holy Cross College, Nagercoil, India"
}
] |
| author_sort | Selvi, V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-05-30T12:44:47Z |
| description | UDC 519.17
We introduce the monophonic global domination number $\overline{\gamma}_m(G)$ by combining monophonic convexity (via chordless paths) with the global domination in a graph and its complement. A monophonic global dominating set is defined, and $\overline{\gamma}_m(G)$ is regarded as the minimum size of sets of this kind. We also establish the bounds, relate $\overline{\gamma}_m(G)$ to the classical domination number, and characterize the graphs that attain extreme values. The realization theorem is proved for prescribed parameter values. The behavior of $\overline{\gamma}_m(G)$ under graph operations, in particular, for the corona product, is analyzed. The applications to the network monitoring are discussed and several open problems are proposed for further research. |
| doi_str_mv | 10.3842/umzh.v78i5-6.7618 |
| first_indexed | 2026-05-30T01:00:36Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7618 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-05-31T01:00:34Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-76182026-05-30T12:44:47Z On the monophonic global domination number of a graph On the monophonic global domination number of a graph Selvi, V. John, J. Flower, V. Sujin Selvi, V. John, J. Flower, V. Sujin monophonic global domination number, global domination number, monophonic number, domination number. Applied Mathematics UDC 519.17 We introduce the monophonic global domination number $\overline{\gamma}_m(G)$ by combining monophonic convexity (via chordless paths) with the global domination in a graph and its complement. A monophonic global dominating set is defined, and $\overline{\gamma}_m(G)$ is regarded as the minimum size of sets of this kind. We also establish the bounds, relate $\overline{\gamma}_m(G)$ to the classical domination number, and characterize the graphs that attain extreme values. The realization theorem is proved for prescribed parameter values. The behavior of $\overline{\gamma}_m(G)$ under graph operations, in particular, for the corona product, is analyzed. The applications to the network monitoring are discussed and several open problems are proposed for further research. УДК 519.17 Про монофонне глобальне число домінування графа Введено число монофонічного глобального домінування $\overline{\gamma}_m(G),$ що поєднує монофонічну опуклість (через безхордові шляхи) та глобальне домінування в графі і його доповненні. Визначено монофонічну глобально домінантну множину, а $\overline{\gamma}_m(G)$ визначено як мінімальна потужність таких множин. Встановлено оцінки та зв'язок $\overline{\gamma}_m(G)$ з класичним числом домінування, а також охарактеризовано графи, на яких досягаються екстремальні значення. Доведено теорему реалізації для наперед заданих значень параметра. Досліджено поведінку $\overline{\gamma}_m(G)$ при операціях над графами, зокрема для коронного добутку. Обговорено застосування до моніторингу мереж і запропоновано низку відкритих задач для подальших досліджень. Institute of Mathematics, NAS of Ukraine 2026-05-29 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7618 10.3842/umzh.v78i5-6.7618 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 5-6 (2026); 379 Український математичний журнал; Том 78 № 5-6 (2026); 379 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7618/10663 Copyright (c) 2026 V. Selvi, J. John, V. Sujin Flower |
| spellingShingle | Selvi, V. John, J. Flower, V. Sujin Selvi, V. John, J. Flower, V. Sujin On the monophonic global domination number of a graph |
| title | On the monophonic global domination number of a graph |
| title_alt | On the monophonic global domination number of a graph |
| title_full | On the monophonic global domination number of a graph |
| title_fullStr | On the monophonic global domination number of a graph |
| title_full_unstemmed | On the monophonic global domination number of a graph |
| title_short | On the monophonic global domination number of a graph |
| title_sort | on the monophonic global domination number of a graph |
| topic_facet | monophonic global domination number global domination number monophonic number domination number. Applied Mathematics |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7618 |
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