Sanming Zhou

collaborators

3 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.CO2026

Perfect codes in Cayley graphs of abelian groups

Peter J. Cameron, Roro Sihui Yap, Sanming Zhou

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

Stability of graph pairs involving cycles

Xiaomeng Wang, Shou-Jun Xu, Sanming Zhou

A graph pair $(I^, I^£)$ is called stable if $\aut(Î)\times\aut(Î£)$ is isomorphic to $\aut(Î\timesÎ£)$ and unstable otherwise, where $I^ \times I^£$ is the direct product of $I^$ an…