پیوندهای مفید
آمار
| تعداد نشریات | 32 |
| تعداد شمارهها | 852 |
| تعداد مقالات | 8,256 |
| تعداد مشاهده مقاله | 52,579,284 |
| تعداد دریافت فایل اصل مقاله | 9,090,023 |
Girth and planarity of the generalized Sierpi\'{n}ski gasket $S[G,t]$ | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).، تیر 2026، صفحه 125-137 اصل مقاله (460.12 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.27933.1690 | ||
| نویسندگان | ||
| F. Attarzadeh* 1؛ A. Abbasi1؛ A. Behtoei2 | ||
| 1Department of pure Mathematics, Faculty of Mathematical Sciences , University of Guilan, Rasht, Iran | ||
| 2Department of Mathematics, Faculty of Science, Imam Khomeini International University,Qazvin, Iran | ||
| چکیده | ||
| Sierpi'{n}ski gasket graphs have many applications and are studied in diverse areas including fractal theory, topology, dynamic systems and chemistry. In this paper we study and determine the girth of generalized Sierpi'{n}ski gasket $S[G, t]$ for an arbitrary simple graph $G$, in terms of the girth of the base graph $G$. Moreover, we determine the planarity of $S[G, t]$ for some famous families of graphs. | ||
| کلیدواژهها | ||
| Girth؛ Planarity؛ Tree؛ Hypercube؛ Sierpi\'{n}ski gasket | ||
| مراجع | ||
|
[1] D. Arett and S. Doree, Coloring and counting on the tower of Hanoi graphs, Math. Mag, 83 (2010), 200-209. [2] F. Attarzadeh, A. Abbasi and M. Gholamnia Taleshani, Some properties of the generalized sierpiński gasket graphs, Trans. Comb, (2) 14 (2025), 97–108. [3] F. Attarzadeh, A. Abbasi and A. Behtoei, Chromatic and Clique number of Generalized Sierpiński Gasket Graph S[G, t], Submitted. [4] G. Della Vecchia and C. Sanges, A recursively scalable network VLSI implementation, Future Gener. Comput. Syst. Sci. Eng, 4 (1988), 235-243. [5] G. Edgar, Measure, Topology and fractal geometry, Springer Verlag, New Yourk, 1990. [6] S. Gravier, M. Kovse and A. Parreau, Generalized Sierpiński graphs, in Posters at Euro-Comb’11, Renyi Institute, Budapest, (2011). [7] S. Gravier, M. Kovˇse, M. Mollard, J. Moncel and A. Parreau, New results on variants of covering codes in Sierpiński graphs, Des. Codes Cryptogr, (2) 69 (2013), 181-188. [8] A. Henke, On p-Kostka numbers and Young modules, European J. Combin, 26 (2005), 923-942. [9] A.M. Hinz, S. Klavzar and S. S. Zemljic, A survey and classification of Sierpiński-type graphs, Discret. Appl. Math, 217 (2017), 565-600. [10] A. M. Hinz, A. Schief, The average distance on the Sierpiński gasket, Probab. Theory Related Fields, 87 (1990), 129-138. [11] M. Jakovac, A 2-parametric generalization of Sierpinski gasket graphs, Ars Combin, 116 (2014), 395-405. [12] M. Jakovac, S. Klavˇzar, Vertex-, edge-, and total-colorings of Sierpiński-like graphs, Discrete Mathematics, 309 (2009), 1548-1556. [13] V. A. Kaimanovich, Random walks on Sierpiński graphs: hyperbolicity and stochastic homogenization, Fractals in Graz, (2003), 145-183. [14] M. Khatibi, A. Behtoei, and F. Attarzadeh, Degree sequence of the generalized Sierpiński graph, Contrib. Discrete Math, 3 (1715-0868) (2020), 88-97. [15] S. Klavˇzar, Coloring Sierpinski graphs and Sierpiński gasket graphs, Taiwan. J. Math, 12 (2008), 513-522. [16] S. Klavˇzar and U. Milutinović, Graphs S(n, k) and a variant of the Tower of Hanoi problem, Czechoslovak Math. J, 122 (1997), 95-104. [17] S. Klavˇzar, U. Milutinović and C. Petr, 1-perfect codes in Sierpiński graphs, Bull. Aust. Math. Soc, (3) 66 (2002), 369-384. [18] F. Klix and K. Rautenstrauch-Goede, Struktur- und Komponenten analyse von Problemlösungsprozessen, Z. Psychol, 174 (1967), 167-193. [19] J. A. Rodriguez-Velaźquez, J. Tomás-Andreu, On the Randić index of polymeric networks modelled by generalized Sierpiński graphs, MATCH Commun. Math. Comput. Chem, 74 (2015), 145-160. [20] J. A. Rodriguez-Velazquez, E. D. Rodriguez-Bazan, A. Estrada-Moreno, On generalized Sierpiński graphs, Discuss. Math. Graph T, (3) 37 (2017), 547-560. [21] D. Romik, Shortest paths in the Tower of Hanoi graph and finite automata, SIAM J. Discrete Math, 20 (2006), 610-622. [22] R. S. Scorer, P. M. Grundy and C.A.B. Smith, Some binary games, Math. Gaz, 28 (1944), 96-103. [23] H. Sydow, Zur metrischen Erfasung von subjektiven Problemzuständen und zu deren Veränderung im Denkprozeb, Z. Psychol, 177 (1970), 145-198. [24] A. M. Teguia and A. P. Godbole, Sierpiński gasket graphs and some of their properties, Australas. J. Combin, 35 (2006), 181-192. [25] A. Teplyaev, Spectral analysis on infinite Sierpiński gaskets, J. Funct. Anal, (2) 159 (1998), 537-567. [26] E. S. Varghese, D. A. Xavier, A. Alsinai, D. Mathew, S. A. Amirtha Raja, H. Ahmed, Strong total monophonic problems in product graphs, networks, and its computational complexity, Journal of Mathematics, (2022), Article ID 6194734, https://doi.org/10.1155/2022/6194734 [27] H. Zhou, M. Tanveer, J. Li, Comparative study of some fixed-point methods in the generation of Julia and Mandelbrot sets, Journal of Mathematics, (2020), Article ID 7020921, https://doi.org/10.1155/2020/7020921 | ||
|
آمار تعداد مشاهده مقاله: 182 تعداد دریافت فایل اصل مقاله: 64 |
||