On the least eigenvalue of genuine strongly 3-walk-regular graphs

Jiahao Zhang, Changxiang He and Rongquan Feng

Applied Mathematics and Computation, 2025, vol. 490, issue C

Abstract: As a generalization of strongly regular graphs, van Dam and Omidi [8] introduced the concept of strongly walk-regular graphs. A graph is called strongly ℓ-walk-regular if the number of walks of length ℓ from a vertex to another vertex depends only on whether the two vertices are adjacent, not adjacent, or identical. They proved that this class of graphs falls into several subclasses including connected regular graphs with four eigenvalues, which are called genuine strongly ℓ-walk-regular. In this paper, we prove that the least eigenvalue of a connected genuine strongly 3-walk-regular graph is no more than −2 and characterize all graphs reaching this upper bound.

Keywords: Eigenvalue; Strongly walk-regular graph; Genuine strongly walk-regular graph (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324006635
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:490:y:2025:i:c:s0096300324006635

DOI: 10.1016/j.amc.2024.129202

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().