Kexiang Xu

activity

20162022

most citedThe general position number of the Cartesian product of two trees

24 citations · 47 across the 12 of their papers we have counts for

collaborators

Showing math.COShow all

12 papers · 1 filter

math.CO2022

New transmission irregular chemical graphs

Kexiang Xu, Jing Tian, Sandi Klavžar

The transmission of a vertex $v$ of a (chemical) graph $G$ is the sum of distances from $v$ to other vertices in $G$ . If any two vertices of $G$ have different transmissions, then…

math.CO2022

On the general position numbers of maximal outerplanar graphs

Jing Tian, Kexiang Xu, Daikun Chao

A subset $R \subseteq V (G)$ of a graph $G$ is a general position set if any triple set $R_{0}$ of $R$ is non-geodesic in $G$ , that is, no vertex of $R_{0}$ lies on any geodesic between…

math.CO2021

Relating the total domination number and the annihilation number for quasi-trees and some composite graphs

Hongbo Hua, Xinying Hua, Sandi Klavžar +1

The total domination number $γ_{t} (G)$ of a graph $G$ is the cardinality of a smallest set $D \subseteq V (G)$ such that each vertex of $G$ has a neighbor in $D$ . The annihilation nu…

math.CO2020★ 24 cited

The general position number of the Cartesian product of two trees

Jing Tian, Kexiang Xu, Sandi Klavžar

The general position number of a connected graph is the cardinality of a largest set of vertices such that no three pairwise-distinct vertices from the set lie on a common shortest…

math.CO2020★ 2 cited

The domination game played on diameter 2 graphs

Csilla Bujtás, Vesna Iršič, Sandi Klavžar +1

Let $γ_{g} (G)$ be the game domination number of a graph $G$ . It is proved that if $diam (G) = 2$ , then $γ_g(G) \le \left\lceil \frac{n(G)}{2} \right\rceil- \left\lfloor \frac{n(…

math.CO2020★ 1 cited

On Rall's $1/2$ -conjecture on the domination game

Csilla Bujtás, Vesna Iršič, Sandi Klavžar +1

The $1/2$ -conjecture on the domination game asserts that if $G$ is a traceable graph, then the game domination number $γ_{g} (G)$ of $G$ is at most $\left\lceil \frac{n(G)}{2} \right\…

math.CO2020★ 1 cited

Constructing new families of transmission irregular graphs

Kexiang Xu, Sandi Klavžar

The transmission of a vertex $v$ of a graph $G$ is the sum of distances from $v$ to all the other vertices in $G$ . A graph is transmission irregular if all of its vertices have pai…

math.CO2019★ 10 cited

Comparison of Wiener index and Zagreb eccentricity indices

Kexiang Xu, Kinkar Chandra Das, Sandi Klavžar +1

The first and the second Zagreb eccentricity index of a graph $G$ are defined as $E_{1} (G) = \sum_{v \in V (G)} ε_{G} (v)^{2}$ and $E_2(G)=\sum_{uv\in E(G)}\varepsilon_{G}(u)\var…

math.CO2019

Comparing Wiener complexity with eccentric complexity

Kexiang Xu, Aleksandar Ilić, Vesna Iršič +2

The transmission of a vertex $v$ of a graph $G$ is the sum of distances from $v$ to all the other vertices in $G$ . The Wiener complexity of $G$ is the number of different transmiss…

math.CO2018

Extremal graphs for vertex-degree-based invariants with given degree sequences

Muhuo Liu, Kexiang Xu, Xiao-Dong Zhang

For a symmetric bivariable function $f (x, y)$ , let the {\it connectivity function} of a connected graph $G$ be $M_{f} (G) = \sum_{uv \in E (G)} f (d (u), d (v))$ , where $d (u)$ is the degree of…

math.CO2017

Embeddings into almost self-centered graphs of given radius

Kexiang Xu, Haiqiong Liu, Kinkar Ch. Das +1

A graph is almost self-centered (ASC) if all but two of its vertices are central. An almost self-centered graph with radius $r$ is called an $r$ -ASC graph. The $r$ -ASC index $θ_r(G…

math.CO2016★ 9 cited

Ordering connected graphs by their Kirchhoff indices

Kexiang Xu, Kinkar Ch. Das, Xiao-Dong Zhang

The Kirchhoff index $K f (G)$ of a graph $G$ is the sum of resistance distances between all unordered pairs of vertices, which was introduced by Klein and Randić. In this paper we ch…