On the spectral moments of trees with a given bipartition

2012/11/21 by Li, Shuchao, Zhang, Jiajia
#05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.4924

Abstract

For two given positive integers p and q with p\leqslant q, we denote \mathscrT_n^{p, q}=T: T is a tree of order n with a (p, q)-bipartition. For a graph G with n vertices, let A(G) be its adjacency matrix with eigenvalues λ₁(G), λ₂(G), ..., λ_n(G) in non-increasing order. The number S_k(G):=∑_i=1ⁿλ_i^k(G) (k=0, 1, ..., n-1) is called the kth spectral moment of G. Let S(G)=(S₀(G), S₁(G),..., S_n-1(G)) be the sequence of spectral moments of G. For two graphs G₁ and G₂, one has G₁\prec_s G₂ if for some k∈ 1,2,...,n-1, S_i(G₁)=S_i(G₂) (i=0,1,...,k-1) and S_k(G₁)

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