A graph G is divisible by a graph H if the characteristic polynomial of G is divisible by that of H. In this paper, a necessary and sufficient condition for recursive graphs to be divisible by a path is used to show that the H-shape graph P2,2;n−42,n−7, known to be (for n large enough) the minimizer of the spectral radius among the graphs of order n and diameter n−5, is determined by its adjacency spectrum if and only if n≠10,13,15.
On the divisibility of H-shape trees and their spectral determination / Chen, Z.; Wang, J.; Brunetti, M.; Belardo, F.. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - 675:(2023), pp. 312-337. [10.1016/j.laa.2023.06.028]
On the divisibility of H-shape trees and their spectral determination
Brunetti M.;Belardo F.
2023
Abstract
A graph G is divisible by a graph H if the characteristic polynomial of G is divisible by that of H. In this paper, a necessary and sufficient condition for recursive graphs to be divisible by a path is used to show that the H-shape graph P2,2;n−42,n−7, known to be (for n large enough) the minimizer of the spectral radius among the graphs of order n and diameter n−5, is determined by its adjacency spectrum if and only if n≠10,13,15.| File | Dimensione | Formato | |
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On the divisibility of H-shape trees and their spectral determination.pdf
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