| Title: | On Vizing's conjecture |
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| Authors: | ID Brešar, Boštjan (Author) |
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| Files: |  Discussiones_Mathematicae_Graph_Theory_2001_Bresar_On_Vizing_s_conjecture.pdf (126,98 KB)
MD5: 286C4062475D3BCDAD7F938289E2AA70
 http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1129
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FKBV - Faculty of Agriculture and Life Sciences
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| Abstract: | A dominating set ▫$D$▫ gor a graph ▫$G$▫ is a subset ▫$V(G)$▫ such that any vertex in ▫$V(G)-D$▫ has a neighbor in ▫$D$▫, and a domination number ▫$\gamma(G)$▫ is the size of a minimum dominating set for ▫$G$▫. For the Cartesian product ▫$G \Box H$▫ Vizing's conjecture states that ▫$\gamma(G \Box H) \ge \gamma(G)\gamma(H)$▫ for every pair of graphs ▫$G,H$▫. In this paper we introduce a new concept which extends the ordinary domination of graphs, and prove that the conjecture holds when ▫$\gamma(G) = \gamma(H) = 3$▫. |
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| Keywords: | mathematics, graph theory, graph, Cartesian product, domination number |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Year of publishing: | 2001 |
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| Number of pages: | str. 5-11 |
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| Numbering: | Letn. 21, št. 1 |
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| PID: | 20.500.12556/DKUM-65351  |
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| ISSN: | 1234-3099 |
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| UDC: | 519.17 |
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| ISSN on article: | 1234-3099 |
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| COBISS.SI-ID: | 11010137 |
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| NUK URN: | URN:SI:UM:DK:PXU92DXH |
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| Publication date in DKUM: | 31.03.2017 |
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| Views: | 1812 |
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| Downloads: | 157 |
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| Metadata: |    |
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| Categories: | Misc.
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