This paper deals with some of the algebraic properties of Sierpinski graphs and a family of regular generalized Sierpinski graphs. For the family of regular generalized Sierpinski graphs, we obtain their spectrum and characterize those graphs that are Cayley graphs. As a by-product, a new family of non-Cayley vertex-transitive graphs, and consequently, a new set of non-Cayley numbers are introduced. We also obtain the Laplacian spectrum of Sierpinski graphs in some particular cases, and make a conjecture on the general case.
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