4 papers
Classification of perfect and total perfect codes in generalized Petersen graphs
Xiaomeng Wang, Junyang Zhang
In a graph , a perfect code is an independent set with the property that every vertex not in is adjacent to a unique vertex in , and a total perfect code is a set …
Perfect codes in circulant graphs of degree
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…
Stability of graph pairs involving cycles
Xiaomeng Wang, Shou-Jun Xu, Sanming Zhou
A graph pair is called stable if $\aut(Γ)\times\aut(Σ)$ is isomorphic to $\aut(Γ\timesΣ)$ and unstable otherwise, where is the direct product of and . A…
On regular sets in Cayley graphs
Xiaomeng Wang, Shou-Jun Xu, Sanming Zhou
Let $\Ga = (V, E)$ be a graph and nonnegative integers. An -regular set in $\Ga$ is a nonempty proper subset of such that every vertex in has exactly …