Binzhou Xia

collaborators

Showing math.COShow all

4 papers · 1 filter

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

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.CO2024

Asymptotic enumeration of Haar graphical representations

Yunsong Gan, Pablo Spiga, Binzhou Xia

This paper represents a significant leap forward in the problem of enumerating vertex-transitive graphs. Recent breakthroughs on symmetry of Cayley (di)graphs show that almost all…