On the Dual Drazin Inverse of Adjacency Matrices of Dual-number-Weighted Digraphs
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| Format: | Preprint |
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2026
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| _version_ | 1866908873633300480 |
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| author | Zhao, Yue Zhang, Daochang Li, Zhongshan Hall, Frank J. |
| author_facet | Zhao, Yue Zhang, Daochang Li, Zhongshan Hall, Frank J. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_08354 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Dual Drazin Inverse of Adjacency Matrices of Dual-number-Weighted Digraphs Zhao, Yue Zhang, Daochang Li, Zhongshan Hall, Frank J. Combinatorics Numerical Analysis 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. |
| title | On the Dual Drazin Inverse of Adjacency Matrices of Dual-number-Weighted Digraphs |
| topic | Combinatorics Numerical Analysis |
| url | https://arxiv.org/abs/2603.08354 |