On the spectral moment of trees with given degree sequences

2012/09/11 by Li Shuchao, Yibing Song, Shuchao, Li +1 · 2 citations
Mathematics · Computer Science · #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1209.2188

Abstract

Let A(G) be the adjacency matrix of graph G 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, G₂, we have G₁\prec_sG₂ if for some k ∈ \1,2,3,...,n-1\, we have S_i(G₁) = S_i(G₂) , i = 0, 1,..., k-1 and S_k(G₁)

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• The Exponential Hyper-Zagreb Indices and Structural Properties of Trees and Bipartite Graphs
• On the spectral moment of graphs with given clique number

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