Xiaomeng Wang

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20242026

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3 papers · 1 filter

math.CO2026

Classification of perfect and total perfect codes in generalized Petersen graphs

Xiaomeng Wang, Junyang Zhang

In a graph $I^$ , a perfect code is an independent set $C$ with the property that every vertex not in $C$ is adjacent to a unique vertex in $C$ , and a total perfect code is a set $C…

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…

math.CO2024

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 $a$ …