| Title: | Maximum independent sets in direct products of cycles or trees with arbitrary graphs |
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| Authors: | ID Paj Erker, Tjaša (Author)
ID Špacapan, Simon (Author) |
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| Files: |  Discussiones_Mathematicae_Graph_Theory_2015_Paj,_Spacapan_Maximum_independent_sets_in_direct_products_of_cycles_or_trees_with_arbitrary.pdf (173,48 KB)
MD5: CB90C497C923333F607088283AF35010
 http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1837
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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: | FS - Faculty of Mechanical Engineering
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| Abstract: | The direct product of graphs ▫$G = (V(G),E(G))$▫ and ▫$H = (V(H),E(H))$▫ is the graph, denoted as ▫$G \times H$▫, with vertex set ▫$V(G \times H) = V(G )\times V(H)$▫, where vertices ▫$(x_1,y_1)$▫ and ▫$(x_2,y_2)$▫ are adjacent in ▫$G \times H$▫ if ▫$x_1x_2 \in E(G)$▫ and ▫$y_1y_2 \in E(H)$▫. Let ▫$n$▫ be odd and ▫$m$▫ even. We prove that every maximum independent set in ▫$P_n \times G$▫, respectively ▫$C_m \times G$▫, is of the form ▫$(A \times C) \cup (B \times D)$▫, where ▫$C$▫ and ▫$D$▫ are nonadjacent in ▫$G$▫, and ▫$A \cup B$▫ is the bipartition of ▫$P_n$▫ respectively ▫$C_m$▫. We also give a characterization of maximum independent subsets of ▫$P_n \times G$▫ for every even ▫$n$▫ and discuss the structure of maximum independent sets in ▫$T \times G$▫ where ▫$T$▫ is a tree. |
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| Keywords: | direct product, independent set |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Year of publishing: | 2015 |
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| Number of pages: | str. 675-688 |
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| Numbering: | Letn. 35, št. 4 |
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| PID: | 20.500.12556/DKUM-65476  |
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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: | 17610841 |
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| NUK URN: | URN:SI:UM:DK:Q8DUGYUA |
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| Publication date in DKUM: | 07.04.2017 |
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| Views: | 1629 |
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| Downloads: | 555 |
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| Metadata: |    |
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| Categories: | Misc.
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