Authors: Stevanović, Dragan 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Ordering Starlike Trees by the Totality of Their Spectral Moments
Journal: Order
Volume: 39
First page: 77
Last page: 94
Issue Date: 2022
Rank: ~M23
ISSN: 0167-8094
DOI: 10.1007/s11083-021-09566-3
Abstract: 
The k-th spectral moment Mk(G) of the adjacency matrix of a graph G represents the number of closed walks of length k in G. We study here the partial order ≼ of graphs, defined by G ≼ H if Mk(G) ≤ Mk(H) for all k ≥ 0, and are interested in the question when is ≼ a linear order within a specified set of graphs? Our main result is that ≼ is a linear order on each set of starlike trees with constant number of vertices. Recall that a connected graph G is a starlike tree if it has a vertex u such that the components of G − u are paths, called the branches of G. It turns out that the ≼ ordering of starlike trees with constant number of vertices coincides with the shortlex order of sorted sequence of their branch lengths.
Keywords: Closed walks | Linear order | Spectral moments | Starlike trees
Publisher: Springer Link

Show full item record

SCOPUSTM   
Citations

1
checked on Nov 8, 2024

Page view(s)

14
checked on Nov 8, 2024

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.