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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| Datum: | 2026 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7618 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
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| DOI: | 10.3842/umzh.v78i5-6.7618 |