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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.12341 |
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| _version_ | 1866917672012218368 |
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| author | Cadavid, Paula Montoya, Mary Luz Rodiño Rodriguez, Pablo M. Vidal, Sebastian J. |
| author_facet | Cadavid, Paula Montoya, Mary Luz Rodiño Rodriguez, Pablo M. Vidal, Sebastian J. |
| contents | A connected graph can be associated with two distinct evolution algebras. In the first case, the structural matrix is the adjacency matrix of the graph itself. In the second case, the structural matrix is the transition probabilities matrix of the symmetric random walk on the same graph. It is well-known that, for a non-singular graph, both evolution algebras are isomorphic if, and only if, the graph is regular or biregular. Moreover, through examples and partial results, it has been conjectured that the same result remains true for singular graphs. The purpose of this work is to provide new examples supporting this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some singular graphs with non-isomorphic associated evolution algebras Cadavid, Paula Montoya, Mary Luz Rodiño Rodriguez, Pablo M. Vidal, Sebastian J. Combinatorics 05C25, 17D92, 05C81 A connected graph can be associated with two distinct evolution algebras. In the first case, the structural matrix is the adjacency matrix of the graph itself. In the second case, the structural matrix is the transition probabilities matrix of the symmetric random walk on the same graph. It is well-known that, for a non-singular graph, both evolution algebras are isomorphic if, and only if, the graph is regular or biregular. Moreover, through examples and partial results, it has been conjectured that the same result remains true for singular graphs. The purpose of this work is to provide new examples supporting this conjecture. |
| title | On some singular graphs with non-isomorphic associated evolution algebras |
| topic | Combinatorics 05C25, 17D92, 05C81 |
| url | https://arxiv.org/abs/2405.12341 |