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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| Main Authors: | , |
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| Format: | Article |
| Language: | fas |
| Published: |
University of Isfahan
2025-05-01
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| Series: | ریاضی و جامعه |
| Subjects: | |
| Online Access: | https://math-sci.ui.ac.ir/article_28563_858755db9d87b4e3493661ba115e2e32.pdf |
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| Summary: | 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. |
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| ISSN: | 2345-6493 2345-6507 |