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arXiv · 2603.08354

On the Dual Drazin Inverse of Adjacency Matrices of Dual-number-Weighted Digraphs

Yue Zhao·Daochang Zhang·Zhongshan Li·Frank J. Hall
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Abstract

The motivation of this paper is to investigate the dual Drazin inverse of adjacency matrices arising from several classes of connected dual-number-weighted digraphs over the dual complex algebra. Explicit formulas for the dual Drazin inverse of dual complex anti-triangular block matrices are derived under suitable assumptions. These results are applied to DN-DS digraphs, DN-DLS digraphs, and DN-DW digraphs. In particular, the assumptions in \cite{AMPMJM2026} are weakened for DN-DS digraphs, an open problem in \cite{AMPMJM2026} for the case $BC=0$ is generalized and solved for DN-DLS digraphs. And the group inverse result in \cite{MNSEJAA2022} for bipartite block form adjacency matrices is extended to the dual Drazin inverse for DN-DW digraphs. We further derive explicit formulas for the dual group inverse and dual Drazin inverse of another adjacency matrix for DN-DW digraphs.

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Yue Zhao, Daochang Zhang, Zhongshan Li, Frank J. Hall. 2026-03-09. On the Dual Drazin Inverse of Adjacency Matrices of Dual-number-Weighted Digraphs. https://arxiv.org/abs/2603.08354

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