Sharp bounds of the A_α-spectral radii of mixed trees

2021/12/03 by Yen-Jen Cheng, Cheng, Yen-Jen, Louis Kao +4
Computer Science · Mathematics · #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.CO #math.SP #msc:05C05 #msc:05C50 #msc:15A42

paper · pdf · doi:10.48550/arxiv.2112.01721

arxiv created 2021/12/03 · arxiv updated 2021/12/06

Abstract

A mixed tree is a tree in which both directed arcs and undirected edges may exist. Let T be a mixed tree with n vertices and m arcs, where an undirected edge is counted twice as arcs. Let A be the adjacency matrix of T. For α∈[0,1], the matrix A_α of T is defined to be αD⁺+(1-α)A, where D⁺ is the the diagonal out-degree matrix of T. The A_α-spectral radius of T is the largest real eigenvalue of A_α. We will give a sharp upper bound and a sharp lower bound of the A_α-spectral radius of T.

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