Girth and planarity of the generalized Sierpi\'{n}ski gasket S[G,t]

‎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.

کلیدواژه ها:

Girth‎ ، ‎Planarity‎ ، ‎Tree‎ ، ‎‎Hypercube‎ ، ‎Sierpi\'{n}ski gasket