Xuanlong Ma

activity

20142023

most citedOn the power graph of a finite group

5 citations · 17 across the 19 of their papers we have counts for

collaborators

20 papers

math.GR2023

Aspects of the commuting graph

V. Arvind, Xuanlong Ma, Peter J. Cameron +1

The commuting graph of a group $G$ is the graph whose vertices are the elements of $G$ , two distinct vertices joined if they commute. Our purpose in this paper is twofold: we discu…

math.CO2022

Perfect codes in quintic Cayley graphs on abelian groups

Yuefeng Yang, Xuanlong Ma, Qing Zeng

A subset $C$ of the vertex set of a graph $Γ$ is called a perfect code of $Γ$ if every vertex of $Γ$ is at distance no more than one to exactly one vertex in $C$ . In this paper, we…

math.GR2021★ 1 cited

Notes on the diameter of the complement of the power graph of a finite group

Xuanlong Ma, Alireza Doostabadi, Kaishun Wang

We determine the diameter of every connected component of the complement of the power graph and the enhanced power graph of a finite group, which completely answers two questions b…

math.CO2021★ 1 cited

Forbidden subgraphs in enhanced power graphs of finite groups

Xuanlong Ma, Samir Zahirović, Yubo Lv +1

The enhanced power graph of a group is the simple graph whose vertex set is consisted of all elements of the group, and whose any pair of vertices are adjacent if they generate a c…

math.CO2021

Completeness-resolvable graphs

Min Feng, Xuanlong Ma, Huiling Xu

Given a connected graph $G = (V (G), E (G))$ , the length of a shortest path from a vertex $u$ to a vertex $v$ is denoted by $d (u, v)$ . For a proper subset $W$ of $V (G)$ , let $m (W)$ be t…

math.CO2020★ 2 cited

The co-prime order graph associated with a finite group

Xuanlong Ma, Zhonghua Wang

Let $G$ be a finite group. The co-prime order graph of $G$ is the graph whose vertex set is $G$ , and two distinct vertices $x, y$ are adjacent if gcd $(o (x), o (y))$ is either $1$ or a…

math.CO2020

Perfect codes in Cayley sum graphs

Xuanlong Ma, Kaishun Wang, Yuefeng Yang

A subset $C$ of the vertex set of a graph $Γ$ is called a perfect code of $Γ$ if every vertex of $Γ$ is at distance no more than one to exactly one vertex in $C$ . Let $A$ be a fini…

math.CO2020

Strong metric dimensions for power graphs of finite groups

Xuanlong Ma, Liangliang Zhai

Let $G$ be a finite group. The order supergraph of $G$ is the graph with vertex set $G$ , and two distinct vertices $x, y$ are adjacent if $o (x) ∣ o (y)$ or $o (y) ∣ o (x)$ . The enh…

math.CO2017

Lambda number of the power graph of a finite group

Xuanlong Ma, Min Feng, Kaishun Wang

The power graph $Γ_{G}$ of a finite group $G$ is the graph with the vertex set $G$ , where two distinct elements are adjacent if one is a power of the other. An $L (2, 1)$ -labeling of…

math.CO2016

The power index of a graph

Xuanlong Ma, Min Feng, Kaishun Wang

The {\em power index} $Θ (Γ)$ of a graph $Γ$ is the least order of a group $G$ such that $Γ$ can embed into the power graph of $G$ . Furthermore, this group $G$ is {\em $Γ$ -optimal}…

math.CO2016

The strong metric dimension of the power graph of a finite group

Xuanlong Ma, Min Feng, Kaishun Wang

We characterize the strong metric dimension of the power graph of a finite group. As applications, we compute the strong metric dimension of the power graph of a cyclic group, an a…

math.GR2016

Finite groups with star-free noncyclic graphs

Xuanlong Ma, Gary L. Walls, Kaishun Wang

For a finite noncyclic group $G$ , let $\Cyc(G)$ be a set of elements $a$ of $G$ such that $⟨ a, b ⟩$ is cyclic for each $b$ of $G$ . The noncyclic graph of $G$ is a graph…

math.GR2015★ 1 cited

Non-cyclic graphs of (non)orientable genus one

Xuanlong Ma

Let $G$ be a finite non-cyclic group. The non-cyclic graph $Γ_{G}$ of $G$ is the graph whose vertex set is $G ∖ C y c (G)$ , two distinct vertices being adjacent if they do not ge…

math.GR2015

Power graphs of (non)orientable genus two

Xuanlong Ma, Gary L. Walls, Kaishun Wang

The power graph $Γ_{G}$ of a finite group $G$ is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. In this paper, we class…

math.CO2015

On the spectra of strong power graphs of finite groups

Xuanlong Ma

We give the characteristic polynomial of the distance or adjacency matrix of the strong power graph of a finite group, and compute its distance and adjacency spectrum.

math.CO2015

Rainbow connectivity of the non-commuting graph of a finite group

Yulong Wei, Xuanlong Ma, Kaishun Wang

Let $G$ be a finite non-abelian group. The non-commuting graph $Γ_{G}$ of $G$ has the vertex set $G ∖ Z (G)$ and two distinct vertices $x$ and $y$ are adjacent if $x y \neq = y x$ , w…

math.CO2014★ 2 cited

The rainbow connection number of the power graph of a finite group

Xuanlong Ma, Min Feng, Kaishun Wang

This paper studies the rainbow connection number of the power graph $Γ_{G}$ of a finite group $G$ . We determine the rainbow connection number of $Γ_{G}$ if $G$ has maximal involutions…

math.GR2014★ 1 cited

On finite groups all of whose cubic Cayley graphs are integral

Xuanlong Ma, Kaishun Wang

For any positive integer $k$ , let $G_{k}$ denote the set of finite groups $G$ such that all Cayley graphs $Cay (G, S)$ are integral whenever $∣ S ∣ \leq k$ . Est${\rm \acute…

math.GR2014★ 4 cited

The full automorphism group of the power (di)graph of a finite group

Min Feng, Xuanlong Ma, Kaishun Wang

We describe the full automorphism group of the power (di)graph of a finite group. As an application, we solve a conjecture proposed by Doostabadi, Erfanian and Jafarzadeh in 2013.

math.CO2014★ 5 cited

On the power graph of a finite group

Min Feng, Xuanlong Ma, Kaishun Wang

The power graph $P_{G}$ of a finite group $G$ is the graph with the vertex set $G$ , where two elements are adjacent if one is a power of the other. We first show that $\math…