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

^*Corresponding author for this work

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

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Abstract

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.

Original language	English
Pages (from-to)	125-137
Number of pages	13
Journal	Linear algebra and its applications
Volume	685
Early online date	5 Jan 2024
DOIs	https://doi.org/10.1016/j.laa.2024.01.003
Publication status	Published - 15 Mar 2024

Keywords

UT-Hybrid-D
Random skew adjacency matrix
Random skew Randić matrix
Skew Randić spectral radius
Skew spectral radius
General random oriented graphs

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title = "The skew spectral radius and skew Randi{\'c} spectral radius of general random oriented graphs",

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.",

keywords = "UT-Hybrid-D, Random skew adjacency matrix, Random skew Randi{\'c} matrix, Skew Randi{\'c} spectral radius, Skew spectral radius, General random oriented graphs",

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

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2024",

month = mar,

day = "15",

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

language = "English",

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T1 - The skew spectral radius and skew Randić spectral radius of general random oriented graphs

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 - UT-Hybrid-D

KW - Random skew adjacency matrix

KW - Random skew Randić matrix

KW - Skew Randić spectral radius

KW - Skew spectral radius

KW - General random oriented graphs

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DO - 10.1016/j.laa.2024.01.003

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SN - 0024-3795

VL - 685

SP - 125

EP - 137

JO - Linear algebra and its applications

JF - Linear algebra and its applications

ER -

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

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