| Naslov: | Partial domination in supercubic graphs |
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| Avtorji: | ID Bujtás, Csilla (Avtor)
ID Henning, Michael A. (Avtor)
ID Klavžar, Sandi (Avtor) |
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| Datoteke: |  URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0012365X23003552
 PDF - Predstavitvena datoteka, prenos (304,87 KB)
MD5: ACE2EBE8F78937B8559A1EBDBF9D5E0F
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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: | For some $\alpha$ with $0 < \alpha \le 1$, a subset $X$ of vertices in a graph $G$ of order $n$ is an $\alpha$-partial dominating set of $G$ if the set $X$ dominates at least $\alpha \times n$ vertices in $G$. The $\alpha$-partial domination number ${\rm pd}_{\alpha}(G)$ of $G$ is the minimum cardinality of an $\alpha$-partial dominating set of $G$. In this paper partial domination of graphs with minimum degree at least $3$ is studied. It is proved that if $G$ is a graph of order $n$ and with $\delta(G)\ge 3$, then ${\rm pd}_{\frac{7}{8}}(G) \le \frac{1}{3}n$. If in addition $n\ge 60$, then ${\rm pd}_{\frac{9}{10}}(G) \le \frac{1}{3}n$, and if $G$ is a connected cubic graph of order $n\ge 28$, then ${\rm pd}_{\frac{13}{14}}(G) \le \frac{1}{3}n$. Along the way it is shown that there are exactly four connected cubic graphs of order $14$ with domination number $5$. |
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| Ključne besede: | domination, partial domination, cubic graphs, supercubic graphs |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.01.2024 |
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| Leto izida: | 2024 |
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| Št. strani: | 11 str. |
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| Številčenje: | Vol. 347, iss. 1, article no. 113669 |
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| PID: | 20.500.12556/DiRROS-18189  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 0012-365X |
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| DOI: | 10.1016/j.disc.2023.113669 |
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| COBISS.SI-ID: | 162890243 |
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| Datum objave v DiRROS: | 15.02.2024 |
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| Število ogledov: | 518 |
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| Število prenosov: | 232 |
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| Metapodatki: |    |
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