| Naslov: | Induced cycles vertex number and $(1,2)$-domination in cubic graphs |
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| Avtorji: | ID Erveš, Rija (Avtor)
ID Tepeh, Aleksandra (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (1,79 MB)
MD5: 328285D2CDB1536D5931222CDCF36A58
 URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0096300325004266
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | 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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| Ključne besede: | cubic graphs, (1, 2)-domination, induced 2-regular subgraphs, induced cycles vertex |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.02.2026 |
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| Leto izida: | 2026 |
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| Št. strani: | 7 str. |
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| Številčenje: | Vol. 510, [article no.] 129700 |
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| PID: | 20.500.12556/DiRROS-23831  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 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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| Opomba: |
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| Datum objave v DiRROS: | 09.10.2025 |
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| Število ogledov: | 240 |
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| Število prenosov: | 115 |
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| Metapodatki: |    |
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