On the Dual Drazin Inverse of Adjacency Matrices of Dual-number-Weighted Digraphs
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 AMPMJM2026 are weakened for DN-DS digraphs, an open problem in AMPMJM2026 for the case BC=0 is generalized and solved for DN-DLS digraphs. And the group inverse result in 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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