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arXiv · 1908.04037

Some Algebraic Properties of Sierpi\'nski-Type Graphs

Mohammad Farrokhi Derakhshandeh Ghouchan·E. Ghorbani·H. R. Maimani·F. Rahimi Mahid
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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.

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Mohammad Farrokhi Derakhshandeh Ghouchan, E. Ghorbani, H. R. Maimani, F. Rahimi Mahid. 2019-08-12. Some Algebraic Properties of Sierpi\'nski-Type Graphs. https://arxiv.org/abs/1908.04037

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