| Title: | Induced cycles vertex number and $(1,2)$-domination in cubic graphs |
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| Authors: | ID Erveš, Rija (Author)
ID Tepeh, Aleksandra (Author) |
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| Files: |  PDF - Presentation file, download (1,79 MB)
MD5: 328285D2CDB1536D5931222CDCF36A58
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0096300325004266
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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
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| Abstract: | A $(1,2)$-dominating set in a graph ▫$G$▫ is a set $S$ such that every vertex outside $S$ has at least one neighbor in $S$, and each vertex in $S$ has at least two neighbors in $S$. The $(1,2)$-domination number, $\gamma_{1, 2}(G)$, is the minimum size of such a set, while $c_{\rm ind}(G)$ is the cardinality of the largest vertex set in that induces one or more cycles. In this paper, we initiate the study of a relationship between these two concepts and discuss how establishing such a connection can contribute to solving a conjecture on the lower bound of $c_{\rm ind}(G)$ for cubic graphs. We also establish an upper bound on $c_{\rm ind}(G)$ for cubic graphs and characterize graphs that achieve this bound. |
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| Keywords: | cubic graphs, (1, 2)-domination, induced 2-regular subgraphs, induced cycles vertex |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.02.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 7 str. |
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| Numbering: | Vol. 510, [article no.] 129700 |
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| PID: | 20.500.12556/DiRROS-23831  |
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| UDC: | 519.17 |
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| ISSN on article: | 1873-5649 |
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| DOI: | 10.1016/j.amc.2025.129700 |
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| COBISS.SI-ID: | 247464963 |
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| Note: |
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| Publication date in DiRROS: | 09.10.2025 |
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| Views: | 230 |
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| Downloads: | 108 |
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| Metadata: |    |
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