Merging the A- and Q-spectral theories for digraphs

2018/10/27 by Weige Xi, Xi, Weige, Wasin So +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #05C50 #15A18 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1810.11669

openalex publication_date 2018/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a digraph and A(G) be the adjacency matrix of G. Let D(G) be the diagonal matrix with outdegrees of vertices of G. For any real α∈[0,1], Liu et al. \citeLWCL defined the matrix A_α(G) as A_α(G)=αD(G)+(1-α)A(G). The largest modulus of the eigenvalues of A_α(G) is called the A_α spectral radius of G. In this paper, we determine the digraphs which attain the maximum (or minimum) A_α spectral radius among all strongly connected digraphs with given parameters such as girth, clique number, vertex connectivity or arc connectivity. We also discuss a number of open problems.

Cited by

• The generalized distance matrix of digraphs
• Some α-spectral extremal results for some digraphs

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