Xiaogang Liu

activity

20232026

collaborators

8 papers

math.CO2026

Fractional revival on oriented Cayley and semi-Cayley graphs over abelian groups

Ming Jiang, Xiaogang Liu, Jing Wang

Fractional revival (FR), a generalization of perfect state transfer (PST), is a significant phenomenon in quantum state transfer that allows quantum information to be transmitted b…

math.CO2025

Pair state transfer in tensor product and double cover

Ming Jiang, Xiaogang Liu, Jing Wang

Quantum state transfer, first introduced by Bose in 2003, is an important physical phenomenon in quantum networks, which plays a vital role in quantum communication and quantum com…

math.CO2025

Enumeration of Cayley graphs over a nonabelian group of order $8 p$

Bei Ye, Xiaogang Liu, Jing Wang

Let $T_{8 p} = ⟨ a, b ∣ a^{2 p} = b^{8} = e, a^{p} = b^{4}, b^{- 1} ab = a^{- 1} ⟩$ be a nonabelian group of order $8 p$ , where $p$ is an odd prime number. In this paper, we give…

math.CO2025

Integral Cayley graphs over a nonabelian group of order $8 n$

Bei Ye, Xiaogang Liu

A graph is called an integral graph when all eigenvalues of its adjacency matrix are integers. We study which Cayley graphs over a nonabelian group $$ T_{8n}=\left\langle a,b\mid a…

math.CO2024

Enumeration of dicirculant digraphs

Jing Wang, Ligong Wang, Xiaogang Liu

Let $T_{4 p} = ⟨ a, b ∣ a^{2 p} = 1, a^{p} = b^{2}, b^{- 1} ab = a^{- 1} ⟩$ be the dicyclic group of order $4 p$ . A Cayley digraph over $T_{4 p}$ is called a dicirculant digraph. In this p…

math.CO2024

Laplacian pair state transfer in Q-graph

Ming Jiang, Xiaogang Liu, Jing Wang

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 st…

math.CO2024

Integral Cayley graphs over a group of order $6 n$

Jing Wang, Xiaogang Liu, Ligong Wang

In this paper, we study the integral Cayley graphs over a non-abelian group $U_{6 n} = ⟨ a, b ∣ a^{2 n} = b^{3} = 1, a^{- 1} ba = b^{- 1} ⟩$ of order $6 n$ . We give a necessary and suf…

math.CO2023

Pretty good fractional revival on Cayley graphs over dicyclic groups

Jing Wang, Ligong Wang, Xiaogang Liu

In this paper, we investigate the existence of pretty good fractional revival on Cayley graphs over dicyclic groups. We first give a necessary and sufficient description for Cayley…

Fractional revival on oriented Cayley and semi-Cayley graphs over abelian groups

Pair state transfer in tensor product and double cover

Enumeration of Cayley graphs over a nonabelian group of order 8p

Integral Cayley graphs over a nonabelian group of order 8n

Enumeration of dicirculant digraphs

Laplacian pair state transfer in Q-graph

Integral Cayley graphs over a group of order 6n

Pretty good fractional revival on Cayley graphs over dicyclic groups

Enumeration of Cayley graphs over a nonabelian group of order $8 p$

Integral Cayley graphs over a nonabelian group of order $8 n$

Integral Cayley graphs over a group of order $6 n$