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Tetravalent one-regular graphs of order p2q2 | ||
Journal of Discrete Mathematics and Its Applications | ||
دوره 8، شماره 2، مهر 2023، صفحه 111-121 اصل مقاله (316.75 K) | ||
نوع مقاله: Full Length Article | ||
شناسه دیجیتال (DOI): 10.22061/jdma.2023.1945 | ||
نویسندگان | ||
Modjtaba Ghorbani؛ Aziz SeyyedHadi؛ Farzaneh Nowroozi-Larki | ||
Department of Mathematics, SRTT University | ||
تاریخ دریافت: 11 اردیبهشت 1402، تاریخ بازنگری: 16 اردیبهشت 1402، تاریخ پذیرش: 22 اردیبهشت 1402 | ||
چکیده | ||
A graph is called one-regular if its full automorphism group acts regularly on the set of arcs. In this paper, we classify all connected one-regular graphs of valency 4 of order $p^2q^2$, where $p>q$ are prime numbers. We also prove that all such graphs are Cayley graphs. | ||
مراجع | ||
[1] Y. G. Baik, Y. Q. Feng, H. S. Sim, M. Y. Xu, On the normality of Cayley graphs of abelian groups, Algebra Colloq. 5(3) (1998) 297–304. [2] N. Biggs, Algebraic Graph Theory, Second edition, Cambridge University Press, Cambridge, 1993. [3] M. D. Burton, Elementary Number Theory,W. C. Brown publishers, 1989. [4] J. D. Dixon, B. Mortimer, Permutation Groups, Springer-Verlag Press, New York, 1996. [5] Y. Q. Feng, K. Kutnar, D. Maruˇsi´c, C. Zhang, Tetravalent one-regular graphs of order 4p2, Filomat 28 (2014) 285–303. [6] A. Gardiner, C. E. Praeger, On 4-valent symmetric graphs, European J. Combin. 15 (1994) 375–381. [7] M. Ghasemi, J. X. Zhou, Tetravalent s-Transitive graphs of order 4p2, Graphs Comb. 29 (2013) 87–97. [8] C. H. Li, Z. Ping Lu, Tetravalent edge−transitive Cayley graphs with odd number of vertices, J. Combin. Theor. Series B 96 (2006) 164–181. [9] I. Martin Isaacs, Finite Group Theory, Graduate Studies in Mathematics Volume 92, American Mathematical Society Providence, Rhode Island, 2008. [10] H. E. Rose, A Course on Finite Groups, Springer-Verlag, 2009. [11] J. J. Rotman, An Introduction to the Theory of Groups, Springer-Verlag, 1995. [12] A. Seyyed-Hadi, M. Ghorbani, F. Nowroozi-Larki, A simple classification of finite groups of order p2q2, Math. Interdisc. 3(2) (2018). [13] M. Suzuki, Group Theroy II, New York, Springer-Verlag, 1985. [14] H.Wielandt, Finite Permutation Groups, Academic Press, New York, 1964. [15] M. Y. Xu, A note on one−regular graphs, Chinese Sci. Bull. 45 (2000) 2160–2162. [16] J. Xu, M. Y. Xu, Arc-transitive Cayley graphs of valency at most four on abelian groups, Southeast Asian Bull. Math. 25 (2001) 355–363. [17] J. X. Zhou, Y-Q.Feng, Tetravalent one−regular graphs of order 2pq, J. Algebraic Combin. 29 (2009) 457–471. | ||
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