## 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_{i}d_{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_{RS}(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 |
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Pages (from-to) | 125-137 |

Number of pages | 13 |

Journal | Linear algebra and its applications |

Volume | 685 |

Early online date | 5 Jan 2024 |

DOIs | |

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