Xuanlong Ma

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20232026

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math.CO2026

Graphs attaining an upper bound on the mixed metric dimension

Shi Chen, Xuanlong Ma

Given a graph $G$ , we show that the mixed metric dimension of $G$ is exactly $ℓ (G) + 2 c (G)$ if and only if $G$ is either a cactus graph in which every cycle has precisely one vert…

math.CO2026

On the mixed metric dimension of $2$ -connected graphs

Shi Chen, Xuanlong Ma

We show that for a $2$ -connected graph $G$ which is not a cycle, the mixed metric dimension of $G$ is at most $2 c (G)$ , where $c (G)$ is the cyclomatic number of $G$ . As an immediate…

math.CO2024

(Total) Perfect codes in (extended) subgroup sum graphs

Xuanlong Ma, Yuefeng Yang, Liangliang Zhai

Given a finite group $G$ with identity $e$ and a normal subgroup $H$ of $G$ , the subgroup sum graph $Γ_{G, H}$ (resp. extended subgroup sum graph $Γ_{G, H}^{+}$ ) of $G$ with respect to…

math.CO2023

Perfect codes in 2-valent Cayley digraphs on abelian groups

Shilong Yu, Yuefeng Yang, Yushuang Fan +1

For a digraph $Γ$ , a subset $C$ of $V (Γ)$ is a perfect code if $C$ is a dominating set such that every vertex of $Γ$ is dominated by exactly one vertex in $C$ . In this paper, we cl…

Graphs attaining an upper bound on the mixed metric dimension

On the mixed metric dimension of 2-connected graphs

(Total) Perfect codes in (extended) subgroup sum graphs

Perfect codes in 2-valent Cayley digraphs on abelian groups

On the mixed metric dimension of $2$ -connected graphs