| Title: | On domination numbers of graph bundles |
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| Authors: | ID Zmazek, Blaž (Author)
ID Žerovnik, Janez (Author) |
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| Files: |  http://www.imfm.si/preprinti/PDF/00998.pdf
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| Language: | English |
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| Work type: | Not categorized |
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| Organization: | PEF - Faculty of Education
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| Abstract: | Let ▫$gamma(G)$▫ be the domination number of a graph ▫$G$▫. It is shown that for any ▫$k ge 0$▫ there exists a Cartesian graph bundle ▫$B Box_varphi F$▫ such that ▫$gamma(B Box_varphi F) = gamma(B)gamma(F) - 2k$▫. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing's conjecture on strong graph bundles is shown not to be true by proving the inequality ▫$gamma(B boxtimes_varphi F) le gamma(B)gamma(F)$▫ for strong graph bundles. Examples of graphs ▫$B$▫ and ▫$F$▫ with ▫$gamma(B boxtimes_varphi F) < gamma(B)gamma(F)$▫ are given. |
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| Keywords: | matematika, teorija grafov, kartezični produkt grafov, dominantno število, dominantna množica, grafovski sveženj, mathematics, graph theory, graph bundle, dominating set, domination number, Cartesian product |
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| Year of publishing: | 2005 |
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| Number of pages: | str. 1-10 |
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| Numbering: | Vol. 43, št. 998 |
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| PID: | 20.500.12556/DKUM-49374  |
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| ISSN: | 1318-4865 |
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| UDC: | 519.17 |
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| COBISS.SI-ID: | 13826905 |
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| NUK URN: | URN:SI:UM:DK:QLKY20QT |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1817 |
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| Downloads: | 114 |
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| Metadata: |    |
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| Categories: | Misc.
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