Sanming Zhou

activity

20162026

most citedPerfect codes in circulant graphs

47 citations · 126 across the 9 of their papers we have counts for

collaborators

9 papers

math.CO2026

Equitable partitions of regular graphs, and perfect sets in normal Cayley graphs

R. A. Bailey, Peter J. Cameron, Sanming Zhou

An equitable partition of a graph $\Ga$ is a partition ${V_{1}, \dots, V_{m}}$ of its vertex set such that for each pair $i, j$ all vertices in $V_{i}$ have the same number of neighbo…

math.CO2025

Perfect codes in Cayley graphs of abelian groups

Peter J. Cameron, Roro Sihui Yap, Sanming Zhou

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.CO2024

Perfect codes in circulant graphs of degree $p^{l} - 1$

Xiaomeng Wang, Oriol Serra, Shou-Jun Xu +1

A perfect code in a graph is an independent set of the graph such that every vertex outside the set is adjacent to exactly one vertex in the set. A circulant graph is a Cayley grap…

math.CO2024

Stability of graph pairs involving cycles

Xiaomeng Wang, Shou-Jun Xu, Sanming Zhou

A graph pair $(Γ, Σ)$ is called stable if $\aut(Γ)\times\aut(Σ)$ is isomorphic to $\aut(Γ\timesΣ)$ and unstable otherwise, where $Γ \times Σ$ is the direct product of $Γ$ and $Σ$ . A…

math.CO2023★ 6 cited

On regular sets in Cayley graphs

Xiaomeng Wang, Shou-Jun Xu, Sanming Zhou

Let $\Ga = (V, E)$ be a graph and $a, b$ nonnegative integers. An $(a, b)$ -regular set in $\Ga$ is a nonempty proper subset $D$ of $V$ such that every vertex in $D$ has exactly $a$ …

math.CO2022★ 35 cited

Corrigendum to "On subgroup perfect codes in Cayley graphs" [European J. Combin. 91 (2021) 103228]

Junyang Zhang, Sanming Zhou

We correct the statements of two theorems and two corollaries in our paper [On subgroup perfect codes in Cayley graphs, European J. Combin. 91 (2021) 103228]. Proofs of these theor…

math.CO2020★ 3 cited

On subgroup perfect codes in Cayley graphs

Junyang Zhang, Sanming Zhou

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.CO2017★ 47 cited

Perfect codes in circulant graphs

Rongquan Feng, He Huang, Sanming Zhou

A perfect code in a graph $Γ = (V, E)$ is a subset $C$ of $V$ that is an independent set such that every vertex in $V ∖ C$ is adjacent to exactly one vertex in $C$ . A total…

math.CO2016★ 35 cited

Total perfect codes in Cayley graphs