Yuan, Shao and Liu proved that the H-shape tree Hn0 = P11,n2;n−−63 minimizes the spectral radius among all graphs with order n > 9 and diameter n−4. In this paper, we achieve the spectral characterization of all graphs in the set H 0 = {Hn0 }n>8. More precisely we show that Hn0 is determined by its spectrum if and only if n 6= 8, 9, 12, and detect all cospectral mates of H80 , H90 and H120 . Divisibility between characteristic polynomials of graphs turns out to be an important tool to reach our goals.
Spectral determination of trees with large diameter and small spectral radius / Gao, X.; Jia, X.; Wang, J.; Brunetti, M.. - In: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION. - ISSN 2538-2128. - 9:4(2024), pp. 607-623. [10.22049/cco.2023.28648.1651]
Spectral determination of trees with large diameter and small spectral radius
Brunetti M.
Ultimo
2024
Abstract
Yuan, Shao and Liu proved that the H-shape tree Hn0 = P11,n2;n−−63 minimizes the spectral radius among all graphs with order n > 9 and diameter n−4. In this paper, we achieve the spectral characterization of all graphs in the set H 0 = {Hn0 }n>8. More precisely we show that Hn0 is determined by its spectrum if and only if n 6= 8, 9, 12, and detect all cospectral mates of H80 , H90 and H120 . Divisibility between characteristic polynomials of graphs turns out to be an important tool to reach our goals.| File | Dimensione | Formato | |
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