| Title: | The core of a vertex transitive complementary prism of a lexicographic product |
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| Authors: | ID Orel, Marko (Author) |
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| Files: |  PDF - Presentation file, download (411,68 KB)
MD5: 3209C9D25F6F6B0222A52580588C4261
 URL - Source URL, visit https://adam-journal.eu/index.php/ADAM/article/view/1623
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | The complementary prism of a graph $\Gamma$ is the graph $\Gamma \overline{\Gamma}$, which is formed from the union of $\Gamma$ and its complement $\overline{\Gamma}$ by adding an edge between each pair of identical vertices in $\Gamma$ and $\overline{\Gamma}$. Vertex-transitive self-complementary graphs provide vertex-transitive complementary prisms. It was recently proved by the author that $\Gamma \overline{\Gamma}$ is a core, i.e. all its endomorphisms are automorphisms, whenever $\Gamma$ is vertex-transitive, self-complementary, and either $\Gamma$ is a core or its core is a complete graph. In this paper the same conclusion is obtained for some other classes of vertex-transitive self-complementary graphs that can be decomposed as a lexicographic product $\Gamma = \Gamma_1 [\Gamma_2]$. In the process some new results aboutthe homomorphisms of a lexicographic product are obtained. |
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| Keywords: | graph homomorphism, core, complementary prism, self-complementary graph, vertex-transitive graph, lexicographic product |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | str. 1-12 |
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| Numbering: | Vol. 6, iss. 3 |
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| PID: | 20.500.12556/DiRROS-18462  |
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| UDC: | 519.17 |
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| ISSN on article: | 2590-9770 |
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| DOI: | 10.26493/2590-9770.1623.7f0 |
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| COBISS.SI-ID: | 145671427 |
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| Note: |
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| Publication date in DiRROS: | 19.03.2024 |
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| Views: | 329 |
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| Downloads: | 166 |
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| Metadata: |     |
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