Zhishuo Zhang

collaborators

4 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 $Γ$ is the direct product $Γ \times K_{2}$ . A graph $Γ$ is said to be stable if all the automorphisms of $Γ \times K_{2}$ come from its factors. Alth…

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…