Quantum fractional revival on zero-divisor graphs over $\mathbb{Z}_n$
Mahidol University（玛希隆大学）；Centre of Excellence in Mathematics, MHESI（数学卓越中心，高等教育委员会）；King Mongkut’s University of Technology Thonburi (KMUTT)（蒙固皇家理工大学）
In this paper, we characterize the existence of perfect state transfer (PST) and fractional revival in continuous-time quantum walks on the zero-divisor graph $Γ(\mathbb{Z}_n)$. By using the canonical equitable partition of $Γ(\mathbb{Z}_n)$ induced by the proper divisors of $n$, we derive a sufficient condition on $n$ for PST to occur between a pair of vertices. We show that fractional revival is restricted to cells of size $2$ within the equitable partition. Furthermore, assuming $-1$ is not an eigenvalue of the quotient spectrum, we establish that two vertices in $Γ(\mathbb{Z}_n)$ are strongly cospectral if and only if they form a cell of size $2$ within the equitable partition that is either a set of false twins or true twins. Finally, we provide a characterization of fractional revival on bipartite $Γ(\mathbb{Z}_n)$ and prove the non-existence of fractional revival on $Γ(\mathbb{Z}_{p^2q})$.
Fractional revival on oriented Cayley and semi-Cayley graphs over abelian groups
School of Mathematics and Statistics,Northwestern Polytechnical University（西北工业大学数学与统计学院）；Xi’an-Budapest Joint Research Center for Combinatorics,Northwestern Polytechnical University（西北工业大学西安-布达佩斯组合学联合研究中心）；School of Mathematics and Statistics,Shaanxi Normal University（陕西师范大学数学与统计学院）
