Sanming Zhou

activity

20122026

most citedCanonical double covers of generalized Petersen graphs, and double generalized Petersen graphs

10 citations · 34 across the 20 of their papers we have counts for

collaborators

22 papers

math.CO2026

The Aldous property for normal Cayley graphs on symmetric groups

Chenhui Lv, Sanming Zhou

Aldous' spectral gap conjecture states that the random walk and the interchange process on any connected graph have the same spectral gap, or, equivalently, the second largest eige…

math.CO2025

Perfect codes in Cayley graphs of Hajós groups

Yusuf Hafidh, Binzhou Xia, Sanming Zhou

A perfect code in a graph $Γ$ is a subset $C$ of the vertex set of $Γ$ such that every vertex of $Γ$ outside $C$ has exactly one neighbour in $C$ . A perfect code in a directed grap…

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.CO2024

A family of symmetric graphs in relation to 2-point-transitive linear spaces

Teng Fang, Sanming Zhou, Shenglin Zhou

A graph $Γ$ is $G$ -symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of arcs of $Γ$ , where an arc is an ordered pair of adjacent vertices. Let $…

math.CO2024

The second largest eigenvalue of some nonnormal Cayley graphs on symmetric groups

Yuxuan Li, Binzhou Xia, Sanming Zhou

A Cayley graph on the symmetric group $S_{n}$ is said to have the Aldous property if its strictly second largest eigenvalue (that is, the largest eigenvalue strictly smaller than the…

math.CO2023★ 3 cited

The second largest eigenvalue of normal Cayley graphs on symmetric groups generated by cycles

Yuxuan Li, Binzhou Xia, Sanming Zhou

We study the normal Cayley graphs $Cay (S_{n}, C (n, I))$ on the symmetric group $S_{n}$ , where $I \subseteq {2, 3, \dots, n}$ and $C (n, I)$ is the set of all cycles in $S_{n}$ with…

math.CO2022

Stability of graph pairs involving vertex-transitive graphs

Yan-Li Qin, Binzhou Xia, Sanming Zhou

A pair of graphs $(Γ, Σ)$ is said to be stable if the full automorphism group of $Γ \times Σ$ is isomorphic to the product of the full automorphism groups of $Γ$ and $Σ$ and unstable…

math.CO2022

A solution to Babai's problem on digraphs with non-diagonalizable adjacency matrix

Yuxuan Li, Binzhou Xia, Sanming Zhou +1

The fact that the adjacency matrix of every finite graph is diagonalizable plays a fundamental role in spectral graph theory. Since this fact does not hold in general for digraphs,…

math.CO2022★ 6 cited

Aldous' spectral gap property for normal Cayley graphs on symmetric groups

Yuxuan Li, Binzhou Xia, Sanming Zhou

Aldous' spectral gap conjecture states that the second largest eigenvalue of any connected Cayley graph on the symmetric group Sn with respect to a set of transpositions is achieve…

math.GR2022

Cubic graphical regular representations of some classical simple groups

Binzhou Xia, Shasha Zheng, Sanming Zhou

A graphical regular representation (GRR) of a group $G$ is a Cayley graph of $G$ whose full automorphism group is equal to the right regular permutation representation of $G$ . In t…

math.CO2021★ 9 cited

Subgroup regular sets in Cayley graphs

Yanpeng Wang, Binzhou Xia, Sanming Zhou

Let $Γ$ be a graph with vertex set $V$ , and let $a$ and $b$ be nonnegative integers. A subset $C$ of $V$ is called an $(a, b)$ -regular set in $Γ$ if every vertex in $C$ has exactly…

math.CO2020★ 4 cited

Stability of pair graphs

Yan-Li Qin, Binzhou Xia, Jin-Xin Zhou +1

We start up the study of the stability of general graph pairs. This notion is a generalization of the concept of the stability of graphs. We say that a pair of graphs $(Γ, Σ)$ is st…

math.CO2020

Regular sets in Cayley graphs

Yanpeng Wang, Binzhou Xia, Sanming Zhou

In a graph $Γ$ with vertex set $V$ , a subset $C$ of $V$ is called an $(a, b)$ -perfect set if every vertex in $C$ has exactly $a$ neighbors in $C$ and every vertex in $V ∖ C$ …

math.CO2019★ 1 cited

An explicit characterization of arc-transitive circulants

Cai Heng Li, Binzhou Xia, Sanming Zhou

A reductive characterization of arc-transitive circulants was given independently by Kovacs in 2004 and the first author in 2005. In this paper, we give an explicit characterizatio…

math.CO2018★ 10 cited

Canonical double covers of generalized Petersen graphs, and double generalized Petersen graphs

Yan-Li Qin, Binzhou Xia, Sanming Zhou

The canonical double cover $\D(Γ)$ of a graph $Γ$ is the direct product of $Γ$ and $K_{2}$ . If $\Aut(\D(Γ))\cong\Aut(Γ)\times\ZZ_2$ then $Γ$ is called stable; otherwise $Γ$ is called…

math.CO2018

Stability of circulant graphs

Yan-Li Qin, Binzhou Xia, Sanming Zhou

The canonical double cover $D (Γ)$ of a graph $Γ$ is the direct product of $Γ$ and $K_{2}$ . If $Aut (D (Γ)) = Aut (Γ) \times Z_{2}$ then $Γ$ is cal…

math.CO2016

Cores of imprimitive symmetric graphs of order a product of two distinct primes

Ricky Rotheram, Sanming Zhou

A retract of a graph $Γ$ is an induced subgraph $Ψ$ of $Γ$ such that there exists a homomorphism from $Γ$ to $Ψ$ whose restriction to $Ψ$ is the identity map. A graph is a core if…

math.CO2016★ 1 cited

Classification of tetravalent $2$ -transitive non-normal Cayley graphs of finite simple groups

Xin Gui Fang, Jie Wang, Sanming Zhou

A graph $Γ$ is called $(G, s)$ -arc-transitive if $G \leq Aut (Γ)$ is transitive on the set of vertices of $Γ$ and the set of $s$ -arcs of $Γ$ , where for an integer $s \geq 1$ …

math.CO2016

Perfect codes in Cayley graphs

He Huang, Binzhou Xia, Sanming Zhou

Given a graph $Γ$ , a subset $C$ of $V (Γ)$ is called a perfect code in $Γ$ if every vertex of $Γ$ is at distance no more than one to exactly one vertex in $C$ , and a subset $C$ of $…

math.GR2016

Vertex-imprimitive symmetric graphs with exactly one edge between any two distinct blocks

Teng Fang, Xin Gui Fang, Binzhou Xia +1

A graph $Γ$ is called $G$ -symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of ordered pairs of adjacent vertices. We give a classification of $…

math.CO2012

Symmetric graphs with 2-arc transitive quotients

Guangjun Xu, Sanming Zhou

A graph $\Ga$ is $G$ -symmetric if $\Ga$ admits $G$ as a group of automorphisms acting transitively on the set of vertices and the set of arcs of $\Ga$, where an arc is an ordered p…

The Aldous property for normal Cayley graphs on symmetric groups

Perfect codes in Cayley graphs of Hajós groups

Which maximal subgroups are perfect codes?

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

A family of symmetric graphs in relation to 2-point-transitive linear spaces

The second largest eigenvalue of some nonnormal Cayley graphs on symmetric groups

The second largest eigenvalue of normal Cayley graphs on symmetric groups generated by cycles

Stability of graph pairs involving vertex-transitive graphs

A solution to Babai's problem on digraphs with non-diagonalizable adjacency matrix

Aldous' spectral gap property for normal Cayley graphs on symmetric groups

Cubic graphical regular representations of some classical simple groups

Subgroup regular sets in Cayley graphs

Stability of pair graphs

Regular sets in Cayley graphs

An explicit characterization of arc-transitive circulants

Canonical double covers of generalized Petersen graphs, and double generalized Petersen graphs

Stability of circulant graphs

Cores of imprimitive symmetric graphs of order a product of two distinct primes

Classification of tetravalent 2-transitive non-normal Cayley graphs of finite simple groups

Perfect codes in Cayley graphs

Vertex-imprimitive symmetric graphs with exactly one edge between any two distinct blocks

Symmetric graphs with 2-arc transitive quotients

Classification of tetravalent $2$ -transitive non-normal Cayley graphs of finite simple groups