Zhishuo Zhang

activity

20232026

collaborators

6 papers

math.CO2026

Asymptotic stability of Cayley graphs on abelian groups

Binzhou Xia, Zhishuo Zhang, Shasha Zheng

For a finite group $G$ , we say that a Cayley graph $Γ$ on $G$ is a most rigid representation (MRR) of $G$ if its full automorphism group has the smallest possible order among all C…

math.CO2025

Which maximal subgroups are perfect codes?

Shouhong Qiao, Ning Su, Binzhou Xia +2

A perfect code in a graph $Γ = (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V ∖ C$ is adjacent to exactly one vertex in $…

math.CO2025

Determining the vertex stabilizers of 4-valent half-arc-transitive graphs

Binzhou Xia, Zhishuo Zhang, Sanming Zhou

We say that a group is a $4$ -HAT-stabilizer if it is the vertex stabilizer of some connected $4$ -valent half-arc-transitive graph. In 2001, Marušič and Nedela proved that every $4$ …

math.CO2025

On subgroup perfect codes in vertex-transitive graphs

Binzhou Xia, Junyang Zhang, Zhishuo Zhang

A subset $C$ of the vertex set $V$ of a graph $Γ$ is called a perfect code in $Γ$ if every vertex in $V ∖ C$ is adjacent to exactly one vertex in $C$ . Given a group $G$ and…

math.CO2024

Isomorphisms of bi-Cayley graphs on generalized quaternion groups

Jin-Hua Xie, Zhishuo Zhang

Let $G$ be a finite group and $S$ be a subset of $G$ . The bi-Cayley graph $BCay (G, S)$ is the graph with vertex set $G \times {0, 1}$ and edge set $\{\{(x,0),(sx,1)\}\mid x…

math.GR2023

A complete classification of shuffle groups

Binzhou Xia, Junyang Zhang, Zhishuo Zhang +1

For positive integers $k$ and $n$ , the shuffle group $G_{k, k n}$ is generated by the $k!$ permutations of a deck of $k n$ cards performed by cutting the deck into $k$ piles with $n$ …