Matrices with simple symmetric digraphs and their group inverses
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866908429021347840 |
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| author | Nandi, Raju |
| author_facet | Nandi, Raju |
| contents | A new class of simple symmetric digraphs called $\mathcal{D}$ is defined and studied here. Any digraph in $\mathcal{D}$ has the property that each non-pendant vertex is adjacent to at least one pendant vertex. A graph theoretical description for the entries of the group inverse of a real square matrix with any digraph belonging to this class is given. We classify all the real square matrices $A$ such that the digraphs associated with $A$ and $A^{\#}$ both are in $\mathcal{D}$, that is, the digraph related to $A$ is either a corona or a star digraph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08691 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Matrices with simple symmetric digraphs and their group inverses Nandi, Raju Combinatorics 05C20 (primary) 05C50, 05C76 (secondary) A new class of simple symmetric digraphs called $\mathcal{D}$ is defined and studied here. Any digraph in $\mathcal{D}$ has the property that each non-pendant vertex is adjacent to at least one pendant vertex. A graph theoretical description for the entries of the group inverse of a real square matrix with any digraph belonging to this class is given. We classify all the real square matrices $A$ such that the digraphs associated with $A$ and $A^{\#}$ both are in $\mathcal{D}$, that is, the digraph related to $A$ is either a corona or a star digraph. |
| title | Matrices with simple symmetric digraphs and their group inverses |
| topic | Combinatorics 05C20 (primary) 05C50, 05C76 (secondary) |
| url | https://arxiv.org/abs/2312.08691 |