Some Algebraic Properties of Sierpi\'nski-Type Graphs
Combinatorics
2020-11-11 v4 Dynamical Systems
Abstract
This paper deals with some of the algebraic properties of Sierpi\'nski graphs and a family of regular generalized Sierpi\'nski graphs. For the family of regular generalized Sierpi\'nski 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 Sierpi\'nski graphs in some particular cases, and make a conjecture on the general case.
Cite
@article{arxiv.1908.04037,
title = {Some Algebraic Properties of Sierpi\'nski-Type Graphs},
author = {Mohammad Farrokhi Derakhshandeh Ghouchan and E. Ghorbani and H. R. Maimani and F. Rahimi Mahid},
journal= {arXiv preprint arXiv:1908.04037},
year = {2020}
}
Comments
16 pages, final version