EIGENVALUES OF LAPLACIANS ON HIGHER DIMENSIONAL VICSEK SET GRAPHS

Shiping Cao (), Robert S. Strichartz () and Melissa Wei
Additional contact information
Shiping Cao: Department of Mathematics, Cornell University, Ithaca 14853, USA
Robert S. Strichartz: Department of Mathematics, Cornell University, Ithaca 14853, USA
Melissa Wei: Department of Mathematics, Cornell University, Ithaca 14853, USA

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-13

Abstract: We study the graphs associated with Vicsek sets in higher dimensional settings. First, we study the eigenvalues of the Laplacians on the approximating graphs of the Vicsek sets, finding a general spectral decimation function. This is an extension of earlier results on two-dimensional Vicsek sets. Second, we study the Vicsek set lattices, which are natural analogues to the Sierpinski lattices. We have a criterion when two different Vicsek set lattices are isomorphic.

Keywords: Vicsek Set; Eigenvalues; Isomorphism of Lattices (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X22500190
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22500190

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X22500190

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().