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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/2407.14376 |
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| _version_ | 1866917727994642432 |
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| author | Jiang, Ming Liu, Xiaogang Wang, Jing |
| author_facet | Jiang, Ming Liu, Xiaogang Wang, Jing |
| contents | In 2018, Chen and Godsil proposed the concept of Laplacian perfect pair state transfer which is a brilliant generalization of Laplacian perfect state transfer. In this paper, we study the existence of Laplacian perfect pair state transfer in the Q-graph of an $r$-regular graph for $r\ge2$. We prove that the Q-graph of an $r$-regular graph does not have Laplacian perfect pair state transfer when $r+1$ is prime or a power of $2$. We also give a sufficient condition for Q-graph to have Laplacian pretty good pair state transfer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14376 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Laplacian pair state transfer in Q-graph Jiang, Ming Liu, Xiaogang Wang, Jing Combinatorics In 2018, Chen and Godsil proposed the concept of Laplacian perfect pair state transfer which is a brilliant generalization of Laplacian perfect state transfer. In this paper, we study the existence of Laplacian perfect pair state transfer in the Q-graph of an $r$-regular graph for $r\ge2$. We prove that the Q-graph of an $r$-regular graph does not have Laplacian perfect pair state transfer when $r+1$ is prime or a power of $2$. We also give a sufficient condition for Q-graph to have Laplacian pretty good pair state transfer. |
| title | Laplacian pair state transfer in Q-graph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.14376 |