Cubic semisymmetric graphs of order $ 40p $
A simple graph $\Gamma$ is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. A simple graph $\Gamma$ is called cubic whenever it is $ 3 $-regular. An important research problem is the classification of semisymmetric cubic graphs of different orders. The purpose of...
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University of Isfahan
2025-05-01
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| Series: | ریاضی و جامعه |
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| Online Access: | https://math-sci.ui.ac.ir/article_28563_858755db9d87b4e3493661ba115e2e32.pdf |
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| author | Mohammad Reza Salarian Javanshir Rezaei |
| author_facet | Mohammad Reza Salarian Javanshir Rezaei |
| author_sort | Mohammad Reza Salarian |
| collection | DOAJ |
| description | A simple graph $\Gamma$ is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. A simple graph $\Gamma$ is called cubic whenever it is $ 3 $-regular. An important research problem is the classification of semisymmetric cubic graphs of different orders. The purpose of this article is the classification of semisymmetric cubic graphs of order $ 40p $, where p is a prime number. We show that for $ p\ne3,31 $ such a graph Does not exist. Suppose p is a prime number, Folkman showed in\cite{fo} that there is no semisymmetric graph of order $ 2p $ or $ 2p^2 $. We show that if $\Gamma$ is a semisymmetric cubic graph of order $ 40p $, then $ p=3 $ and $\Gamma$ is isomorphic to a semisymmetric cubic graph of order $ 120 $ or $ p=31 $ and $\Gamma$ is isomorphic to the coset graph $ C(L_2 (31):\mathbb{S}_4,\mathbb{S}_4).$ Our basic tools in this research are automorphism of graphs, simple groups, solevable groups and permutation groups. |
| format | Article |
| id | doaj-art-6597537a8d5146339bb7f4df50bca393 |
| institution | Kabale University |
| issn | 2345-6493 2345-6507 |
| language | fas |
| publishDate | 2025-05-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | ریاضی و جامعه |
| spelling | doaj-art-6597537a8d5146339bb7f4df50bca3932025-08-20T03:48:13ZfasUniversity of Isfahanریاضی و جامعه2345-64932345-65072025-05-0110112514410.22108/msci.2024.140259.163928563Cubic semisymmetric graphs of order $ 40p $Mohammad Reza Salarian0Javanshir Rezaei1Deparement of Mathematics,,Faculty of Mathematical and Cumputer Science Kharazmi, ,Tehran,.IranStudent of ,,Faculty of Mathematical and Cumputer Science Kharazmi, ,Tehran, ,IranA simple graph $\Gamma$ is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. A simple graph $\Gamma$ is called cubic whenever it is $ 3 $-regular. An important research problem is the classification of semisymmetric cubic graphs of different orders. The purpose of this article is the classification of semisymmetric cubic graphs of order $ 40p $, where p is a prime number. We show that for $ p\ne3,31 $ such a graph Does not exist. Suppose p is a prime number, Folkman showed in\cite{fo} that there is no semisymmetric graph of order $ 2p $ or $ 2p^2 $. We show that if $\Gamma$ is a semisymmetric cubic graph of order $ 40p $, then $ p=3 $ and $\Gamma$ is isomorphic to a semisymmetric cubic graph of order $ 120 $ or $ p=31 $ and $\Gamma$ is isomorphic to the coset graph $ C(L_2 (31):\mathbb{S}_4,\mathbb{S}_4).$ Our basic tools in this research are automorphism of graphs, simple groups, solevable groups and permutation groups.https://math-sci.ui.ac.ir/article_28563_858755db9d87b4e3493661ba115e2e32.pdfsemisymmetric graphsymmetric graphvertex-transiyive graphedge-transitive graphautomorphissm of graph |
| spellingShingle | Mohammad Reza Salarian Javanshir Rezaei Cubic semisymmetric graphs of order $ 40p $ ریاضی و جامعه semisymmetric graph symmetric graph vertex-transiyive graph edge-transitive graph automorphissm of graph |
| title | Cubic semisymmetric graphs of order $ 40p $ |
| title_full | Cubic semisymmetric graphs of order $ 40p $ |
| title_fullStr | Cubic semisymmetric graphs of order $ 40p $ |
| title_full_unstemmed | Cubic semisymmetric graphs of order $ 40p $ |
| title_short | Cubic semisymmetric graphs of order $ 40p $ |
| title_sort | cubic semisymmetric graphs of order 40p |
| topic | semisymmetric graph symmetric graph vertex-transiyive graph edge-transitive graph automorphissm of graph |
| url | https://math-sci.ui.ac.ir/article_28563_858755db9d87b4e3493661ba115e2e32.pdf |
| work_keys_str_mv | AT mohammadrezasalarian cubicsemisymmetricgraphsoforder40p AT javanshirrezaei cubicsemisymmetricgraphsoforder40p |