Zhishuo Zhang

activity

20242026

collaborators

6 papers

math.CO2026

Almost all standard double covers of abelian Cayley graphs have smallest possible automorphism groups

Binzhou Xia, Zhishuo Zhang, Shasha Zheng

The standard double cover of a graph $I^$ is the direct product $I^ \times K_{2}$ . A graph $I^$ is said to be stable if all the automorphisms of $I^ \times K_{2}$ come from its factors.…

math.CO2025

Which maximal subgroups are perfect codes?

Shouhong Qiao, Ning Su, Binzhou Xia +2

A perfect code in a graph $I^ = (V, E)$ 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, MaruÅ¡iÄ and Nedela proved that every $…

math.CO2025

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.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 $I^$ is called a perfect code in $I^$ if every vertex in $V ∖ C$ is adjacent to exactly one vertex in $C$ . Given a group $G$ an…

math.GR2024

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 $n$ …