Harmonic signed trees

Qian Yu and Yaoping Hou

Applied Mathematics and Computation, 2024, vol. 475, issue C

Abstract: A signed graph G˙ is defined to be harmonic if its net-degree vector d±(G˙) is a zero vector or an eigenvector of adjacency matrix A(G˙) corresponding to an eigenvalue λ. In this paper, we demonstrate the existence of λ-harmonic signed trees with arbitrary diameter and the nonexistence of finite 0-harmonic signed trees. And we determine all harmonic signed trees with diameter at most 5. Moreover, we give some general properties of finite harmonic signed trees. In particular, a 1-harmonic signed tree must be 1 net-regular.

Keywords: Harmonic graph; Signed graph; Tree (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324002169
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:475:y:2024:i:c:s0096300324002169

DOI: 10.1016/j.amc.2024.128744

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 ().