Spectral extremal results on the α-index of graphs without minors and star forests

2022/04/01 by Mingzhu Chen, Chen, Ming-Zhu, A-Ming Liu +3
Computer Science · Mathematics · #05C35 #05C50 #05C83 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2204.00181

openalex publication_date 2022/04/01 · openalex created_date 2022/05/01 · openalex updated_date 2026/07/28

Abstract

Let G be a graph of order n, and let A(G) and D(G) be the adjacency matrix and the degree matrix of G respectively. Define the convex linear combinations A_α(G) of A (G) and D (G) by A_α(G)=αD(G)+(1-α)A(G) for any real number 0≤α≤1. The α-index of G is the largest eigenvalue of A_α(G). In this paper, we determine the maximum α-index and characterize all extremal graphs for K_r minor-free graphs, K_s,t minor-free graphs, and star-forest-free graphs for any 0

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