## Abstract

The A_{α}-matrix of a digraph G is defined as A_{α}(G)=αD^{+}(G)+(1−α)A(G), where α∈[0,1), D^{+}(G) is the diagonal outdegree matrix and A(G) is the adjacency matrix. The k-th A_{α} spectral moment of G is defined as ∑_{i=1} ^{n}λ_{αi} ^{k}, where λ_{αi} are the eigenvalues of the A_{α}-matrix of G, and k is a nonnegative integer. In this paper, we obtain the digraphs which attain the minimal and maximal second A_{α} spectral moment (also known as the A_{α} energy) within classes of digraphs with a given dichromatic number. We also determine sharp bounds for the third A_{α} spectral moment within the special subclass which we define as join digraphs. These results are related to earlier results about the second and third Laplacian spectral moments of digraphs.

Original language | English |
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Pages (from-to) | 77-103 |

Number of pages | 27 |

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
- Dichromatic
- Laplacian spectral moment
- A spectral moment

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