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On unimodular tricyclic graphs with a unique perfect matching | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 خرداد 1405 اصل مقاله (497.39 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30800.2622 | ||
| نویسندگان | ||
| Parameswar Basumatary1؛ Debajit Kalita* 2 | ||
| 1Department of Mathematics, Salbari College, Salbari, Baksa, BTC, Assam-781318, India | ||
| 2Department of Mathematical Sciences, Tezpur University, Napaam, Sonitpur, Assam-784028, India | ||
| چکیده | ||
| A graph is called unimodular if the determinant of its adjacency matrix is $\pm1$. Akbari and Kirkland [\textit{Linear Algebra and its Applications}, 421(1):3--15, 2007.] proved that a unicyclic graph is unimodular precisely when it has a unique perfect matching. However, a bicyclic or tricyclic graph with a unique perfect matching need not be unimodular. Recently, Basumatary and Sarma [\textit{Discrete Applied Mathematics}, 346:49-61, 2024.] characterized those bicyclic graphs with a unique perfect matching that are unimodular. In this article, we identify which tricyclic graphs with a unique perfect matching possess the unimodularity property. Our results provide a complete characterization of such graphs. | ||
| کلیدواژهها | ||
| Adjacency matrix؛ Unique perfect matching؛ Tricyclic graph؛ Unimodular graph | ||
| مراجع | ||
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[1] S. Akbari and S.J. Kirkland, On unimodular graphs, Linear Algebra Appl. 421 (2007), no. 1, 3–15. https://doi.org/10.1016/j.laa.2006.10.017
[2] P. Basumatary and K. Sarma, On unimodular graphs with a unique perfect matching, Discrete Appl. Math. 346 (2024), 49–61. https://doi.org/10.1016/j.dam.2023.12.008
[3] C. Berge, The Theory of Graphs, Methuen & Co. Ltd, London, 1962.
[4] P. Camion, Characterization of totally unimodular matrices, Proc. Amer. Math. Soc. 16 (1965), no. 5, 1068–1073. https://doi.org/10.2307/2035618 [5] R Chandrasekaran, Total unimodularity of matrices, SIAM J. Appl. Math. 17 (1969), no. 6, 1032–1034. https://doi.org/10.1137/0117092
[6] F.G. Commoner, A sufficient condition for a matrix to be totally unimodular, Networks 3 (1973), no. 4, 351–365. https://doi.org/10.1002/net.3230030406 [7] D. de Werra, On some characterisations of totally unimodular matrices, Math. Program. 20 (1981), no. 1, 14–21. https://doi.org/10.1007/BF01589329 [8] I. Heller and C.B. Tompkins, An extension of a theorem of dantzig’s, Linear Inequalities and Related Systems.(AM-38) 38 (2016), 247–254. https://doi.org/10.1515/9781400881987-015
[9] A.J. Hoffman and J.B. Kruskal, Integral boundary points of convex polyhedra, 50 Years of Integer Programming 1958-2008: From the Early Years to the State-of-the-Art, Springer, 2009, pp. 49–76. https://doi.org/10.1007/978-3-540-68279-0_3
[10] M.W. Padberg, A note on the total unimodularity of matrices, Discrete Math. 14 (1976), no. 3, 273–278. https://doi.org/10.1016/0012-365X(76)90041-8
[11] D. Ye, Y. Yang, B. Mandal, and D.J. Klein, Graph invertibility and median eigenvalues, Linear Algebra Appl. 513 (2017), 304–323. https://doi.org/10.1016/j.laa.2016.10.020
[12] Z. Zhu and Q. Yu, The number of independent sets of tricyclic graphs, Appl. Math. Lett. 25 (2012), no. 10, 1327–1334. https://doi.org/10.1016/j.aml.2011.11.038 | ||
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آمار تعداد مشاهده مقاله: 10 تعداد دریافت فایل اصل مقاله: 12 |
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