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

Jiayu Lou; Ligong Wang; Ming Yuan

doi:10.1016/j.dam.2023.06.026

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

Jiayu Lou, Ligong Wang, Ming Yuan

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 [Formula presented] among all minimally 2-connected graphs with given order or size, respectively.

Original language	English
Pages (from-to)	281-291
Number of pages	11
Journal	Discrete Applied Mathematics
Volume	339
DOIs	https://doi.org/10.1016/j.dam.2023.06.026
State	Published - 15 Nov 2023

Keywords

Extremal graph
Minimally 2-connected graph
α-index

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10.1016/j.dam.2023.06.026

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title = "On the α-index of minimally 2-connected graphs with given order or size",

abstract = "For any real α∈[0,1], Nikiforov defined the Aα-matrix of a graph G as Aα(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 Aα(G) is called the α-index or the Aα-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 [Formula presented] among all minimally 2-connected graphs with given order or size, respectively.",

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AU - Lou, Jiayu

AU - Wang, Ligong

AU - Yuan, Ming

PY - 2023/11/15

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N2 - For any real α∈[0,1], Nikiforov defined the Aα-matrix of a graph G as Aα(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 Aα(G) is called the α-index or the Aα-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 [Formula presented] among all minimally 2-connected graphs with given order or size, respectively.

AB - For any real α∈[0,1], Nikiforov defined the Aα-matrix of a graph G as Aα(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 Aα(G) is called the α-index or the Aα-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 [Formula presented] among all minimally 2-connected graphs with given order or size, respectively.

KW - Extremal graph

KW - Minimally 2-connected graph

KW - α-index

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M3 - 文章

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JO - Discrete Applied Mathematics

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

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