| Title: | Edge-transitive lexicographic and cartesian products |
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| Authors: | ID Imrich, Wilfried (Author)
ID Iranmanesh, Ali (Author)
ID Klavžar, Sandi (Author)
ID Soltani, Abolghasem (Author) |
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| Files: |  Discussiones_Mathematicae_Graph_Theory_2016_Imrich_et_al._Edge-transitive_lexicographic_and_Cartesian_products.pdf (150,33 KB)
MD5: 69CDEAAAF474E8D160D243D46BBD6A32
 http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1892
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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: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product ▫$G \circ H$▫ of a connected graph ▫$G$▫ that is not complete by a graph ▫$H$▫, we show that it is edge-transitive if and only if ▫$G$▫ is edge-transitive and ▫$H$▫ is edgeless. If the first factor of ▫$G \circ H$▫ is non-trivial and complete, then ▫$G \circ H$▫ is edge-transitive if and only if ▫$H$▫ is the lexicographic product of a complete graph by an edgeless graph. This fixes an error of Li, Wang, Xu, and Zhao (Appl. Math. Lett. 24 (2011) 1924--1926). For the Cartesian product it is shown that every connected Cartesian product of at least two non-trivial factors is edge-transitive if and only if it is the Cartesian power of a connected, edge- and vertex-transitive graph. |
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| Keywords: | edge-transitive graph, vertex-transitive graph, lexicographic product of graphs, Cartesian product of graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 16.04.2015 |
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| Article acceptance date: | 29.12.2015 |
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| Publication date: | 29.12.2015 |
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| Publisher: | University of Zielona Góra |
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| Year of publishing: | 2016 |
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| Number of pages: | Str. 857-865 |
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| Numbering: | Letn. 36, št. 4 |
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| PID: | 20.500.12556/DKUM-65337  |
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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: | 17777241 |
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| NUK URN: | URN:SI:UM:DK:HWK1G8VH |
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| Publication date in DKUM: | 31.03.2017 |
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| Views: | 1202 |
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| Downloads: | 464 |
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| Metadata: |    |
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| Categories: | Misc.
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