The skew spectral radius and skew Randić spectral radius of general random oriented graphs

Dan Hu; Hajo Broersma; Jiangyou Hou; Shenggui Zhang

doi:10.1016/j.laa.2024.01.003

The skew spectral radius and skew Randić spectral radius of general random oriented graphs

Dan Hu, Hajo Broersma, Jiangyou Hou, Shenggui Zhang

数学与统计学院

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

Let G be a simple connected graph on n vertices, and let G^σ be an orientation of G with skew adjacency matrix S(G^σ). Let d_i be the degree of the vertex v_i in G. The skew Randić matrix of G^σ is the n×n real skew symmetric matrix R_S(G^σ)=[(R_S)_ij], where (R_S)_ij=−(R_S)_ji=(d_id_j)^{−[Formula presented]} if (v_i,v_j) is an arc of G^σ, and (R_S)_ij=(R_S)_ji=0 otherwise. The skew spectral radius ρ_S(G^σ) and the skew Randić spectral radius ρ_{R_S}(G^σ) of G^σ are defined as the spectral radius of S(G^σ) and R_S(G^σ) respectively. In this paper we give upper bounds for the skew spectral radius and skew Randić spectral radius of general random oriented graphs.

源语言	英语
页（从-至）	125-137
页数	13
期刊	Linear Algebra and Its Applications
卷	685
DOI	https://doi.org/10.1016/j.laa.2024.01.003
出版状态	已出版 - 15 3月 2024

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abstract = "Let G be a simple connected graph on n vertices, and let Gσ be an orientation of G with skew adjacency matrix S(Gσ). Let di be the degree of the vertex vi in G. The skew Randi{\'c} matrix of Gσ is the n×n real skew symmetric matrix RS(Gσ)=[(RS)ij], where (RS)ij=−(RS)ji=(didj)−[Formula presented] if (vi,vj) is an arc of Gσ, and (RS)ij=(RS)ji=0 otherwise. The skew spectral radius ρS(Gσ) and the skew Randi{\'c} spectral radius ρRS(Gσ) of Gσ are defined as the spectral radius of S(Gσ) and RS(Gσ) respectively. In this paper we give upper bounds for the skew spectral radius and skew Randi{\'c} spectral radius of general random oriented graphs.",

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author = "Dan Hu and Hajo Broersma and Jiangyou Hou and Shenggui Zhang",

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day = "15",

doi = "10.1016/j.laa.2024.01.003",

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AU - Hu, Dan

AU - Broersma, Hajo

AU - Hou, Jiangyou

AU - Zhang, Shenggui

PY - 2024/3/15

Y1 - 2024/3/15

N2 - Let G be a simple connected graph on n vertices, and let Gσ be an orientation of G with skew adjacency matrix S(Gσ). Let di be the degree of the vertex vi in G. The skew Randić matrix of Gσ is the n×n real skew symmetric matrix RS(Gσ)=[(RS)ij], where (RS)ij=−(RS)ji=(didj)−[Formula presented] if (vi,vj) is an arc of Gσ, and (RS)ij=(RS)ji=0 otherwise. The skew spectral radius ρS(Gσ) and the skew Randić spectral radius ρRS(Gσ) of Gσ are defined as the spectral radius of S(Gσ) and RS(Gσ) respectively. In this paper we give upper bounds for the skew spectral radius and skew Randić spectral radius of general random oriented graphs.

AB - Let G be a simple connected graph on n vertices, and let Gσ be an orientation of G with skew adjacency matrix S(Gσ). Let di be the degree of the vertex vi in G. The skew Randić matrix of Gσ is the n×n real skew symmetric matrix RS(Gσ)=[(RS)ij], where (RS)ij=−(RS)ji=(didj)−[Formula presented] if (vi,vj) is an arc of Gσ, and (RS)ij=(RS)ji=0 otherwise. The skew spectral radius ρS(Gσ) and the skew Randić spectral radius ρRS(Gσ) of Gσ are defined as the spectral radius of S(Gσ) and RS(Gσ) respectively. In this paper we give upper bounds for the skew spectral radius and skew Randić spectral radius of general random oriented graphs.

KW - General random oriented graphs

KW - Random skew adjacency matrix

KW - Random skew Randić matrix

KW - Skew Randić spectral radius

KW - Skew spectral radius

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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The skew spectral radius and skew Randić spectral radius of general random oriented graphs

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