آمار
| تعداد نشریات | 5 |
| تعداد شماره‌ها | 108 |
| تعداد مقالات | 1,228 |
| تعداد مشاهده مقاله | 1,148,339 |
| تعداد دریافت فایل اصل مقاله | 1,007,663 |
2-semi equivelar maps on the torus and the Klein bottle with few vertices | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 بهمن 1402 اصل مقاله (736.49 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29269.1919 | ||
| نویسندگان | ||
| Anand Kumar Tiwari* 1؛ Yogendra Singh2؛ Amit Tripathi3 | ||
| 1Department of Applied Science, Indian Institute of Information Technology, Allahabad 211 015, India | ||
| 2Department of Mathematics and Statistics, Vignan's Foundation for Science, Technology & Research, Vadlamudi 522213, India | ||
| 3Department of Applied Science & Humanities, Rajkiya Engineering College, Banda 210201, India | ||
| چکیده | ||
| The $k$-semi equivelar maps, for $k \geq 2$, are generalizations of maps on the surfaces of Johnson solids to closed surfaces other than the 2-sphere. In the present study, we determine 2-semi equivelar maps of curvature 0 exhaustively on the torus and the Klein bottle. Furthermore, we classify (up to isomorphism) all these 2-semi equivelar maps on the surfaces with up to 12 vertices. | ||
| کلیدواژه‌ها | ||
| 2-Semi equivelar maps؛ Face-sequence؛ Torus؛ Klein bottle | ||
| مراجع | ||
|
[1] U. Brehm, Polyhedral Maps with Few Edges, Topics in Combinatorics and Graph Theory: Essays in Honour of Gerhard Ringel, Springer, 1990, pp. 153–162.
[2] U. Brehm and W. K¨uhnel, Equivelar maps on the torus, Eur. J. Comb. 29 (2008), no. 8, 1843–1861. https://doi.org/10.1016/j.ejc.2008.01.010 [3] D. Chavey, Tilings by regular polygons—II, Comput. Math. Appl. 17 (1989), no. 1–3, 147–165. https://doi.org/10.1016/0898-1221(89)90156-9 [4] B. Datta and D. Maity, Semi-equivelar and vertex-transitive maps on the torus, Beitr. Algebra Geom. 58 (2017), no. 3, 617–634. https://doi.org/10.1007/s13366-017-0332-z [5] B. Datta and D. Maity, Platonic solids, archimedean solids and semi-equivelar maps on the sphere, Discrete Math. 345 (2022), no. 1, Article ID: 112652. https://doi.org/10.1016/j.disc.2021.112652 [6] B. Datta and N. Nilakantan, Equivelar polyhedra with few vertices, Discrete Comput. Geom. 26 (2001), no. 3, 429–461. https://doi.org/10.1007/s00454-001-0008-0 [7] B. Datta and A.K. Upadhyay, Degree-regular triangulations of torus and klein bottle, Proc. Math. Sci. 115 (2005), no. 3, 279–307. https://doi.org/10.1007/BF02829658 [8] B. Grünbaum and G.C. Shephard, Tilings and Patterns, Courier Dover Publications, New York, 1987.
[9] J. Karabáš and R. Nedela, Archimedean solids of genus two, Electron. Notes Discrete Math. 28 (2007), 331–339. https://doi.org/10.1016/j.endm.2007.01.047 [10] J. Karabáš and R. Nedela, Archimedean maps of higher genera, Math. Comp. 81 (2012), 569–583. https://doi.org/10.1090/S0025-5718-2011-02502-0 [11] W. Kurth, Enumeration of platonic maps on the torus, Discrete Math. 61 (1986), no. 1, 71–83. https://doi.org/10.1016/0012-365X(86)90029-4 [12] T. Réti, E. Bitay, and Z. Kosztol´anyi, On the polyhedral graphs with positive combinatorial curvature, Acta Polytech. Hung. 2 (2005), no. 2, 19–37.
[13] Y. Singh and A.K. Tiwari, Doubly semi-equivelar maps on the plane and the torus, AKCE Int. J. Graphs Comb. 19 (2022), no. 3, 296–310. https://doi.org/10.1080/09728600.2022.2146549 [14] Y. Singh and A.K. Tiwari, Enumeration of doubly semi-equivelar maps on the klein bottle, Indian J. Pure Appl. Math. (2023), 1–24. https://doi.org/10.1007/s13226-023-00503-1 [15] A.K. Tiwari, Y. Singh, and A. Tripathi, 2-semi-equivelar maps on the torus and the klein bottle with few vertices, (2022).
[16] A.K. Tiwari and A.K. Upadhyay, Semi-equivelar maps on the torus and the klein bottle with few vertices, Math. Slovaca. 67 (2017), no. 2, 519–532. https://doi.org/10.1515/ms-2016-0286 [17] A.K. Tiwari and A.K. Upadhyay, Semi-equivelar maps on the surface of euler characteristic−1, Note Mat. 37 (2018), no. 2, 91–102. https://doi.org/10.1285/i15900932v37n2p91 [18] A.K. Upadhyay, A.K. Tiwari, and D. Maity, Semi-equivelar maps, Beitr. Algebra Geom. 55 (2014), no. 1, 229–242. https://doi.org/10.1007/s13366-012-0130-6 [19] L. Zhang, A result on combinatorial curvature for embedded graphs on a surface, Discrete Math. 308 (2008), no. 24, 6588–6595. https://doi.org/10.1016/j.disc.2007.11.007 | ||
|
آمار تعداد مشاهده مقاله: 140 تعداد دریافت فایل اصل مقاله: 653 |
||