| Title: | The domination and independent domination numbers of some families of snarks |
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| Authors: | ID Pereira, Alessandra A. (Author)
ID Campos, Christiane N. (Author) |
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| Files: |  AMC_Pereira,Campos_2025.pdf (505,21 KB)
MD5: A93AD7DA5203FDEB1D6D5E320C0B8D70
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | A dominating set of a graph G is a set S ⊆ V (G) such that every vertex in V (G) either belongs to S or is adjacent to some vertex in S. The domination number is the minimum cardinality of a dominating set of G. An independent dominating set of G is a dominating set that is also independent. The minimum cardinality of an independent dominating set of G is the independent domination number of G. Given the computational complexity of these problems, extensive research has been done on finding bounds or determining these parameters for classes of graphs, especially cubic graphs. Furthermore, determining how far apart these parameters are is also a challenging problem. In this work, we establish some bounds for the domination number and the independent domination number for families of cubic graphs, in particular for Generalized Blanuša Snarks and for two families of
Loupekine Snarks known as LP_0-snarks and LP_1-snarks. We also show that the parameters are equal for these graphs and conjecture that this equality holds for every snark. |
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| Keywords: | domination, independent domination, Generalized Blanuša Snarks, Loupekine Snarks |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 29.04.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 15 str. |
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| Numbering: | Vol. 25, no. 3, [article no.] P3.01 |
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| PID: | 20.500.12556/RUP-21996  |
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| ISBN: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | https://doi.org/10.26493/1855-3974.3285.dc4 |
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| Publication date in RUP: | 21.10.2025 |
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| Views: | 397 |
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| Downloads: | 10 |
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