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Automorphism group of quasi-abelian semi-Cayley graphs | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 8، شماره 1، شهریور 2023، صفحه 43-48 اصل مقاله (248.27 K) | ||
| نوع مقاله: Special Issue of JDMA in the Memory of Prof. Ali Reza Ashrafi | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2023.10137.1059 | ||
| نویسنده | ||
| Majid Arezoomand* | ||
| Department of Mathematics, Larestan University | ||
| تاریخ دریافت: 08 بهمن 1401، تاریخ بازنگری: 17 بهمن 1401، تاریخ پذیرش: 01 اسفند 1401 | ||
| چکیده | ||
| Let G be a group and R,L,S be subsets of G such that $R=R^{-1}$, $L=L^{-1}$ and $1\notin R\cup L$. The undirected graph $\SC(G;R,L,S)$ with vertex set union of $G_1=\{g_1\mid g\in G\}$ and $G_2=\{g_2\mid g\in G\}$, and edge set the union of $\{\{g_1,(gr)_1\}\mid g\in G, r\in R\}$, $\{\{g_2,(gl)_2\}\mid g\in G,l\in L\}$ and $\{\{g_1,(gs)_2\}\mid g\in G,s\in S\}$ is called semi-Cayley graph over G. We say that $\SC(G;R,L,S)$ is quasi-abelian if R,L and S are a union of conjugacy classes of G. In this paper, we study the automorphism group of quasi-abelian semi-Cayley graphs. | ||
| کلیدواژه‌ها | ||
| Semi-Cayley graph؛ quasi-abelian semi-Cayley graph؛ automorphism of graph | ||
| مراجع | ||
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[1] M. Arezoomand, B. Taeri, A classification of finite groups with integral bi-Cayley graphs, Trans. Combin. 4(4) (2015) 55-61. [2] M. Arezoomand, B. Taeri, Isomorphisms of finite semi-Cayley graphs, Acta Math. Sinica, Engl. Ser. 31(4) (2015) 715-730. [3] M. Arezoomand, M. Ghasemi, Normality of one matching semi-Cayley graphs over finite abelia groups with maximum degree three, Contribution. Discrete Math. 15(3) (2019) 75-87. [4] M. Arezoomand, A note on the eigenvalues of n-Cayley graphs, Mat. Vesn. 72 (2020) 351-357. [5] M. Arezoomand, Perfect state transfer semi-Cayley graphs over abelian groups, Linear Multilinear Algebra (2022). https://doi.org/10.1080/03081087.2022.2101602. [6] X. Gao, Y. Luo, The spectrum of semi-Cayley graphs over abelian groups, Linear Algebra Appl.432 (2010) 2974-2983. [7] W. Imrich, Graphs with transitive abelian automorphism group, in Combinatorial Theory and its Applications, P. Erdös et al. eds., Coll. Math. Soc. János Bolyai 4, Balatonfüred, Hungary 4 (1969) 651–656. [8] I. Kovacs, A. Malniˇ c, D. Maruˇ siˇ c, ˇ S. Miklaviˇ c, One-matching bi-Cayley graphs over abelian groups, European J. Combin. 30 (2009) 602-616. [9] M. J. de Resmini, D. Jungnickel, Strongly regular semi-Cayley graphs, J. Algebraic Combin. 1 (1992) 217-228. [10] S. Wang, M. Arezoomand, T. Feng, Perfect state transfer on quasi-abelian semi-Cayley graphs, submitted. [11] S. Wang, M. Arezoomand, T. Feng, Algebraic degrees of quasi-abelian semi-Cayley graphs, sub-mitted. | ||
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