| Title: | Roman domination of cartesian bundles of cycles over cycles |
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| Authors: | ID Brezovnik, Simon (Author)
ID Žerovnik, Janez (Author) |
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| Files: |  PDF - Presentation file, download (314,36 KB)
MD5: B8F274F259679427F09893DC0A550FA5
 URL - Source URL, visit https://www.mdpi.com/2227-7390/13/15/2351
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
 RUDOLFOVO - Rudolfovo - Science and Technology Centre Novo Mesto
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| Abstract: | A Roman dominating function $f$ of a graph $G(V, E)$ assigns labels from the set $\{0,1,2\}$ to vertices such that every vertex labeled $0$ has a neighbor labeled $2$. The weight of an RDF $f$ is defined as $w(f) = \sum_{v \in V} f(v)$, and the Roman domination number, $\gamma_R(G)$, is the minimum weight among all RDFs of $G$. This paper studies the domination and Roman domination numbers in Cartesian bundles of cycles. Furthermore, the constructed optimal patterns improve known bounds and suggest even better bounds might be achieved by combining patterns, especially for bundles involving shifts of order $4k$ and $5k$. |
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| Keywords: | Roman domination, domination, graph bundles, Roman graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 1-18 |
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| Numbering: | Vol. 13, iss. 15, [art. no.] 2351 |
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| PID: | 20.500.12556/DiRROS-23352  |
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| UDC: | 519.17 |
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| ISSN on article: | 2227-7390 |
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| DOI: | 10.3390/math13152351 |
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| COBISS.SI-ID: | 243736579 |
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| Note: | Nasl. z nasl. zaslona;
Opis vira z dne 24. 7. 2025;
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| Publication date in DiRROS: | 21.08.2025 |
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| Views: | 266 |
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| Downloads: | 147 |
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| Metadata: |    |
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