On the α-index of minimally 2-connected graphs with given order or size

2022/11/02 by Jiayu Lou, Lou, Jiayu, Ligong Wang +3
Computer Science · Materials Science · Mathematics · #05C35 #05C40 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Phase-change materials and chalcogenides

paper · pdf · doi:10.48550/arxiv.2301.03389

openalex publication_date 2022/11/02 · openalex created_date 2023/01/11 · openalex updated_date 2026/07/28

Abstract

For any real α∈ [0,1], Nikiforov defined the A_α-matrix of a graph G as A_α(G)=αD(G)+(1-α)A(G), where A(G) and D(G) are the adjacency matrix and the diagonal matrix of vertex degrees of G, respectively. The largest eigenvalue of A_α(G) is called the α-index or the A_α-spectral radius of G. A graph is minimally k-connected if it is k-connected and deleting any arbitrary chosen edge always leaves a graph which is not k-connected. In this paper, we characterize the extremal graphs with the maximum α-index for α∈ [(1)/(2),1) among all minimally 2-connected graphs with given order or size, respectively.

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