The existence of a \P₂,C₃,P₅,T(3)\-factor based on the size or the A_α-spectral radius of graphs

2024/12/16 by X. Y. Zhang, Lihua You, Zhang, Xianglong +1
Computer Science · Engineering · Mathematics · #05C35 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2412.11580

openalex publication_date 2024/12/16 · openalex created_date 2024/12/18 · openalex updated_date 2026/07/28

Abstract

Let G be a connected graph of order n. A \P₂,C₃,P₅,T(3)\-factor of G is a spanning subgraph of G such that each component is isomorphic to a member in \P₂,C₃,P₅,T(3)\, where T(3) is a \1,2,3\-tree. The A_α-spectral radius of G is denoted by ρ_α(G). In this paper, we obtain a lower bound on the size or the A_α-spectral radius for α∈[0,1) of G to guarantee that G has a \P₂,C₃,P₅,T(3)\-factor, and construct an extremal graph to show that the bound on A_α-spectral radius is optimal.

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