ON THE α-INDEX OF MINIMALLY k-(EDGE-)CONNECTED GRAPHS FOR SMALL k

Jiayu Lou; Ligong Wang; Ming Yuan

doi:10.4134/BKMS.b240112

ON THE α-INDEX OF MINIMALLY k-(EDGE-)CONNECTED GRAPHS FOR SMALL k

Jiayu Lou
, Ligong Wang
, Ming Yuan

数学与统计学院

Northwestern Polytechnical University Xian

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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 (Formula present), respectively.

源语言	英语
页（从-至）	961-975
页数	15
期刊	Bulletin of the Korean Mathematical Society
卷	62
期	4
DOI	https://doi.org/10.4134/BKMS.b240112
出版状态	已出版 - 7月 2025

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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 Aα-matrix of a graph G as Aα(G) = αD(G) + (1 − α)A(G). The largest eigenvalue of Aα(G) is called the α-index or the Aα-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 (Formula present), respectively.",

keywords = "Minimally 2-edge-connected graph, extremal graph, minimally 3-connected graph, α-index",

author = "Jiayu Lou and Ligong Wang and Ming Yuan",

note = "Publisher Copyright: {\textcopyright} 2025 Korean Mathematical Society.",

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AU - Lou, Jiayu

AU - Wang, Ligong

AU - Yuan, Ming

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N2 - 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 Aα-matrix of a graph G as Aα(G) = αD(G) + (1 − α)A(G). The largest eigenvalue of Aα(G) is called the α-index or the Aα-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 (Formula present), respectively.

AB - 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 Aα-matrix of a graph G as Aα(G) = αD(G) + (1 − α)A(G). The largest eigenvalue of Aα(G) is called the α-index or the Aα-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 (Formula present), respectively.

KW - Minimally 2-edge-connected graph

KW - extremal graph

KW - minimally 3-connected graph

KW - α-index

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M3 - 文章

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JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 4

ER -

ON THE α-INDEX OF MINIMALLY k-(EDGE-)CONNECTED GRAPHS FOR SMALL k

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