Some algebraic properties of Sierpiński-type graphs - Farrokhi Derakhshandeh Ghouchan,, Mohammad (Ars mathematica contemporanea, 2021)
This paper deals with some of the algebraic properties of Sierpiński graphs and a family of regular generalized Sierpiński graphs. For the family of regular generalized Sierpiński 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 Sierpiński graphs in some particular cases, and make a conjecture on the general case.
Keywords: Cayley graph; Cayleyjev graf; graf Sierpińskega; Laplaceov operator; Laplacian; ne-Cayleyjevo število; non-Cayley number; Sierpiński graph; spectrum; spekter