Periodicity and perfect state transfer of Grover walks on quadratic unitary Cayley graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915438561067008 |
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| author | Bhakta, Koushik Bhattacharjya, Bikash |
| author_facet | Bhakta, Koushik Bhattacharjya, Bikash |
| contents | The quadratic unitary Cayley graph $\mathcal{G}_{\mathbb{Z}_n}$ has vertex set $\mathbb{Z}_n: =\{0,1, \ldots ,n-1\}$, where two vertices $u$ and $v$ are adjacent if and only if $u - v$ or $v-u$ is a square of some units in $\mathbb{Z}_n$. This paper explores the periodicity and perfect state transfer of Grover walks on quadratic unitary Cayley graphs. We determine all periodic quadratic unitary Cayley graphs. From our results, it follows that there are infinitely many integral as well as non-integral graphs that are periodic. Additionally, we also determine the values of $n$ for which the quadratic unitary Cayley graph $\mathcal{G}_{\mathbb{Z}_n}$ exhibits perfect state transfer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08715 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periodicity and perfect state transfer of Grover walks on quadratic unitary Cayley graphs Bhakta, Koushik Bhattacharjya, Bikash Combinatorics 05C50, 81Q99 The quadratic unitary Cayley graph $\mathcal{G}_{\mathbb{Z}_n}$ has vertex set $\mathbb{Z}_n: =\{0,1, \ldots ,n-1\}$, where two vertices $u$ and $v$ are adjacent if and only if $u - v$ or $v-u$ is a square of some units in $\mathbb{Z}_n$. This paper explores the periodicity and perfect state transfer of Grover walks on quadratic unitary Cayley graphs. We determine all periodic quadratic unitary Cayley graphs. From our results, it follows that there are infinitely many integral as well as non-integral graphs that are periodic. Additionally, we also determine the values of $n$ for which the quadratic unitary Cayley graph $\mathcal{G}_{\mathbb{Z}_n}$ exhibits perfect state transfer. |
| title | Periodicity and perfect state transfer of Grover walks on quadratic unitary Cayley graphs |
| topic | Combinatorics 05C50, 81Q99 |
| url | https://arxiv.org/abs/2408.08715 |