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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