Xuanlong Ma

activity

20232026

collaborators

7 papers

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.GR2026

The diameter and dominating sets of the difference graph of a nilpotent group

Xuanlong Ma, Samir Zahirović, Katarina Žigerović

Given a finite group $G$ , the difference graph of $G$ , denoted by $D (G)$ , is the difference of the enhanced power graph of $G$ and the power graph of $G$ , with all isolat…

math.GR2025

On finite groups whose coprime graph is a divisor graph

Xuanlong Ma, Liangliang Zhai, Nan Gao +1

In this paper, we first characterize which generalized lexicographic products are divisor graphs. As applications, we show that power graphs, reduced power graphs and order graphs…

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.GR2024

Forbidden subgraphs on conjugacy class graphs of groups

Papi Ray, Sonakshee Arora, Xuanlong Ma

Let $G$ be a finite group. The commuting (resp. nilpotent) conjugacy class graph $Γ_{C C C} (G)$ (resp. $Γ_{N C C} (G)$ ) of $G$ is a simple graph whose vertex set consists of all non-cen…

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…