Some algebraic properties of Sierpiński-type graphs

Mohammad Farrokhi Derakhshandeh Ghouchan, Ebrahim Ghorbani, Hamid Reza Maimani, Farhad Rahimi Mahid

Abstract


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


Sierpiński graph, spectrum, Laplacian, Cayley graph, non-Cayley number

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DOI: https://doi.org/10.26493/1855-3974.2199.97e

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications