| Title: | The 2-rainbow domination number of Cartesian product of cycles |
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| Authors: | ID Brezovnik, Simon (Author)
ID Rupnik Poklukar, Darja (Author)
ID Žerovnik, Janez (Author) |
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| Files: |  URL - Source URL, visit https://amc-journal.eu/index.php/amc/article/view/3168
 PDF - Presentation file, download (393,84 KB)
MD5: EA8A18D6474DE6B5EB1D54C8F4381CAE
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  RUDOLFOVO - Rudolfovo - Science and Technology Centre Novo Mesto
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| Abstract: | A k-rainbow dominating function (kRDF) of G is a function that assigns subsets of {1, 2, ..., k} to the vertices of G such that for vertices v with f(v) = ∅ we have Uu∈N(v)f(u) = {1, 2, ..., k}. The weight w(f) of a kRDF f is defined as w(f) = P v∈V(G)|f(v)|. The minimum weight of a kRDF of G is called the k-rainbow domination number of G, which is denoted by γrk(G). In this paper, we study the 2-rainbow domination number of the Cartesian product of two cycles. Exact values are given for a number of infinite families and we prove lower and upper bounds for all other cases. |
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| Keywords: | 2-rainbow domination, domination number, cartesian product |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 16.05.2025 |
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| Publisher: | Društvo matematikov, fizikov in astronomov, Društvo matematikov, fizikov in astronomov, Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije |
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| Year of publishing: | 2025 |
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| Number of pages: | 17 str. |
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| Numbering: | Vol. 25, no. 3 |
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| PID: | 20.500.12556/DiRROS-24206  |
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| UDC: | 519.17 |
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| ISSN on article: | 1855-3966 |
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| DOI: | 10.26493/1855-3974.3168.74d |
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| COBISS.SI-ID: | 212017155 |
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| Publication date in DiRROS: | 21.11.2025 |
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| Views: | 126 |
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| Downloads: | 77 |
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