On the α-index of minimally k-(edge-)connected graphs for small k

2023/06/13 by Lou, Jiayu, Wang, Ligong, Yuan, Ming
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.07793

Abstract

Let G be a graph with adjacency matrix A(G) and let D(G) be the diagonal matrix of vertex degrees of G. 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). 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-(edge)-connected if it is k-(edge)-connected and deleting any arbitrary chosen edge always leaves a graph which is not k-(edge)-connected. In this paper, we characterize the minimally 2-edge-connected graphs and minimally 3-connected graph with given order having the maximum α-index for α∈ [(1)/(2),1), respectively.

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