University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 Girth and planarity of the generalized Sierpi\'{n}ski gasket $S[G,t]$ 125 137 8824 10.22124/jart.2025.27933.1690 EN F. Attarzadeh Department of pure Mathematics, Faculty of Mathematical Sciences , University of Guilan, Rasht, Iran A. Abbasi Department of pure Mathematics, Faculty of Mathematical Sciences , University of Guilan, Rasht, Iran A. Behtoei Department of Mathematics, Faculty of Science, Imam Khomeini International University,Qazvin, Iran Journal Article 2024 07 14 ‎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 ‎$‎G‎$‎‎.<br />‎Moreover‎, ‎we determine the planarity of $S[G‎, ‎t]$ for some famous families of graphs‎. https://jart.guilan.ac.ir/article_8824_148bfb4bef2545d4aadfc3982ffa1570.pdf