Perfect state transfer on graphs with clusters
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918263930224640 |
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| author | Monterde, Hermie Pal, Hiranmoy |
| author_facet | Monterde, Hermie Pal, Hiranmoy |
| contents | Using graphs with clusters, we provide a unified approach for constructing graphs with pair state transfer-relative to the adjacency, Laplacian, and signless Laplacian matrix-between the same pair of states at the same time, despite being non-regular. We show that for each $k\geq 5$, there are infinitely many connected graphs with maximum valency $k$ admitting this property. This framework also aids in establishing sufficient conditions for pair state transfer in edge-perturbed graphs, including complete graphs and complete bipartite graphs. Furthermore, we utilize graph products to generate new infinite families of graphs with the above property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perfect state transfer on graphs with clusters Monterde, Hermie Pal, Hiranmoy Combinatorics Quantum Physics 05C50, 81P45 Using graphs with clusters, we provide a unified approach for constructing graphs with pair state transfer-relative to the adjacency, Laplacian, and signless Laplacian matrix-between the same pair of states at the same time, despite being non-regular. We show that for each $k\geq 5$, there are infinitely many connected graphs with maximum valency $k$ admitting this property. This framework also aids in establishing sufficient conditions for pair state transfer in edge-perturbed graphs, including complete graphs and complete bipartite graphs. Furthermore, we utilize graph products to generate new infinite families of graphs with the above property. |
| title | Perfect state transfer on graphs with clusters |
| topic | Combinatorics Quantum Physics 05C50, 81P45 |
| url | https://arxiv.org/abs/2505.07982 |