On the divisibility of H-shape trees and their spectral determination

2023/05/03 by Zhen Chen, Chen, Zhen, Jianfeng Wang +5 · 1 citation
Mathematics · Engineering · Computer Science · #Graph theory and applications #graph theory and CDMA systems #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.2305.02146

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 P_2,2;n-4^2,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.

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• A Characterization of Trees with Trinomial Partial Petrial Polynomials

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