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Automorphism group of a graph constructed from a lattice | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقاله 2، دوره 9، شماره 3، آذر 2024، صفحه 173-179 اصل مقاله (260.37 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2024.11157.1082 | ||
| نویسندگان | ||
| Shahide Malekpour* 1؛ Behnam Bazigaran2 | ||
| 1Department of Mathematics | ||
| 2Department of Mathematics, University of Kashan | ||
| تاریخ دریافت: 21 مرداد 1403، تاریخ پذیرش: 04 شهریور 1403 | ||
| چکیده | ||
| Let $L$ be a lattice and $S$ be a $\wedge$-closed subset of $L$. The graph $\Gamma_{S}(L)$ is a simple graph with all elements of $L$ as vertex set and two distinct vertex $x,y$ are adjacent if and only if $x\vee y\in S$. In this paper, we verify the automorphism group of $\Gamma_{S}(L)$ and the relation by automorphism group of the lattice $L$. Also we study some properties of the graph $\Gamma_{S}(L)$ where $S$ is a prime filter or an ideal such as the perfect maching. | ||
| کلیدواژه‌ها | ||
| Automorphism group of a graph؛ prime filter؛ automorphism group of a lattice؛ perfect maching of a graph | ||
| مراجع | ||
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[1] M. Afkhami, Z. Barati, K. Khashayarmanesh, A graph associated to a lattice, Ric. Mat. 63 (2014) 67–78. [2] M. Alizadeh, A. K. Das, H. R. Maimani, M. R. Pouranki, S. Yassemi, On the diameter and girth of zero-divisor graphs of posets, Discrete Appl. Math. 160 (2012) 1319–1324. [3] J. A. Bondy, U. S. R. Murty, Graph Theory with Applications, American Elsevier Publishing Co. Inc. New York, 1976. [4] T. Donnellan, Lattice Theory, Pergamon Press, Oxford-New York-Toronto, Ont. 1968 [5] G. Gratzer, Lattice Theory: Foundation, Birkh ¨ auser/Springer Basel AG, Basel, 2011. ¨ [6] R. Halas, H. Langer, The zero divisor graph of a qoset, Order 27 (2010) 343–351. [7] V. V. Joshi, A. U. Khiste, On the zero divisor graphs of pm-lattices, Discrete Math 312 (2012) 2076– 2082. [8] R. Hammack, W. Imrich, S. Klavˇzar, Handbook of Product Graph, Second edition. with a foreword by Peter Winkler. Discrete Mathematics and its Applications, Boca Raton, CRC Press, Boca Raton, FL, 2011. [9] S. Malekpour, B. Bazigaran, On Realizability of Graphs as ΓS(L) for some Lattice L, Southeast Asian Bull. Math. 43 (2019) 537–551. [10] S. Malekpour, B. Bazigaran, Some properties of a graph associated to a lattice, Quasigroups and Related Systems 24 (2016) 93–102. [11] L. Rodriguez, Automorphism groups of simple graphs, Mathematics (2014) 1–25. [12] K. Samei, The zero divisor graph of a reduced ring, J. Pure and Appl. Algebra 209 (2007) 813–821. | ||
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