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

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