Drazin Inverses and Walk Structure of Oriented Dutch Windmill Graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908889918734336 |
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| author | Araújo, C. Mendes Maciala, Faustino Patrício, Pedro |
| author_facet | Araújo, C. Mendes Maciala, Faustino Patrício, Pedro |
| contents | We investigate the Drazin invertibility of adjacency matrices associated with a class of oriented graphs known as oriented Dutch windmill graphs. By analyzing walks of prescribed lengths and exploiting the structure of the minimal polynomial, we obtain explicit expressions for the Drazin inverse and determine its index. The approach combines combinatorial enumeration with algebraic matrix analysis, offering a constructive characterization that generalizes known results for paths, cycles, and bipartite graphs. Beyond its intrinsic theoretical value, the framework provides insight into discrete models governed by cyclic feedback and may serve as a basis for symbolic computation of generalized inverses in structured networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15543 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Drazin Inverses and Walk Structure of Oriented Dutch Windmill Graphs Araújo, C. Mendes Maciala, Faustino Patrício, Pedro Combinatorics Rings and Algebras 15A09, 15A10, 05C20 We investigate the Drazin invertibility of adjacency matrices associated with a class of oriented graphs known as oriented Dutch windmill graphs. By analyzing walks of prescribed lengths and exploiting the structure of the minimal polynomial, we obtain explicit expressions for the Drazin inverse and determine its index. The approach combines combinatorial enumeration with algebraic matrix analysis, offering a constructive characterization that generalizes known results for paths, cycles, and bipartite graphs. Beyond its intrinsic theoretical value, the framework provides insight into discrete models governed by cyclic feedback and may serve as a basis for symbolic computation of generalized inverses in structured networks. |
| title | Drazin Inverses and Walk Structure of Oriented Dutch Windmill Graphs |
| topic | Combinatorics Rings and Algebras 15A09, 15A10, 05C20 |
| url | https://arxiv.org/abs/2603.15543 |