Some algebraic properties of Sierpiński-type graphs

Authors

DOI:

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

Keywords:

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

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.

Published

2021-10-21

Issue

Section

Articles