Cong X. Kang

activity

20112024

most citedIteration Index of a Zero Forcing Set in a Graph

31 citations · 143 across the 21 of their papers we have counts for

collaborators

Showing math.COShow all

21 papers · 1 filter

math.CO2024★ 1 cited

On Distance and Strong Metric Dimension of the Modular Product

Cong X. Kang, Aleksander Kelenc, Iztok Peterin +1

The modular product $G ⋄ H$ of graphs $G$ and $H$ is a graph on vertex set $V (G) \times V (H)$ . Two vertices $(g, h)$ and $(g^{'}, h^{'})$ of $G ⋄ H$ are adjacent if $g = g^{'}$ and $…

math.CO2023

Maker-Breaker Strong Resolving Game

Cong X. Kang, Aleksander Kelenc, Eunjeong Yi

Let $G$ be a graph with vertex set $V$ . A set $S \subseteq V$ is a \emph{strong resolving set} of $G$ if, for distinct $x, y \in V$ , there exists $z \in S$ such that either $x$ lies o…

math.CO2022

Maker-Breaker Metric Resolving Games on Graphs

Cong X. Kang, Eunjeong Yi

Let $d (x, y)$ denote the length of a shortest path between vertices $x$ and $y$ in a graph $G$ with vertex set $V$ . For a positive integer $k$ , let $d_{k} (x, y) = min {d (x, y), k + 1}$ an…

math.CO2021★ 1 cited

Distance- $k$ locating-dominating sets in graphs

Cong X. Kang, Eunjeong Yi

Let $G$ be a graph with vertex set $V$ , and let $k$ be a positive integer. A set $D \subseteq V$ is a \emph{distance- $k$ dominating set} of $G$ if, for each vertex $u \in V - D$ , the…

math.CO2021

The Simultaneous Fractional Dimension of Graph Families

Cong X. Kang, Iztok Peterin, Eunjeong Yi

A subset $S$ of the vertices $V$ of a connected graph $G$ resolves $G$ if no two vertices of $V$ share the same list of distances (shortest-path metric) with respect to the vertice…

math.CO2020

Maker-Breaker resolving game

Cong X. Kang, Sandi Klavžar, Ismael G. Yero +1

A set of vertices $W$ of a graph $G$ is a resolving set if every vertex of $G$ is uniquely determined by its vector of distances to $W$ . In this paper, the Maker-Breaker resolving…

math.CO2019

On Laplacian Monopoles

Cong X. Kang, Gretchen L. Matthews, Justin D. Peachey

We consider the action of the (combinatorial) Laplacian of a finite and simple graph on integer vectors. By a \emph{Laplacian monopole} we mean an image vector negative at exactly…

math.CO2018★ 17 cited

The connected metric dimension at a vertex of a graph

Linda Eroh, Cong X. Kang, Eunjeong Yi

The notion of metric dimension, $d im (G)$ , of a graph $G$ , as well as a number of variants, is now well studied. In this paper, we begin a local analysis of this notion by introduci…

math.CO2017★ 7 cited

The fractional $k$ -metric dimension of graphs

Cong X. Kang, Ismael G. Yero, Eunjeong Yi

Let $G$ be a graph with vertex set $V (G)$ . For any two distinct vertices $x$ and $y$ of $G$ , let $R {x, y}$ denote the set of vertices $z$ such that the distance from $x$ to $z$ i…

math.CO2016★ 15 cited

The fractional strong metric dimension in three graph products

Cong X. Kang, Ismael G. Yero, Eunjeong Yi

For any two distinct vertices $x$ and $y$ of a graph $G$ , let $S {x, y}$ denote the set of vertices $z$ such that either $x$ lies on a $y - z$ geodesic or $y$ lies on an $x - z$ geode…

math.CO2014

On Domination Number and Distance in Graphs

Cong X. Kang

A vertex set $S$ of a graph $G$ is a \emph{dominating set} if each vertex of $G$ either belongs to $S$ or is adjacent to a vertex in $S$ . The \emph{domination number} $γ (G)$ of $G$ …

math.CO2014★ 28 cited

A Comparison between the Metric Dimension and Zero Forcing Number of Trees and Unicyclic Graphs

Linda Eroh, Cong X. Kang, Eunjeong Yi

The \emph{metric dimension} $dim (G)$ of a graph $G$ is the minimum number of vertices such that every vertex of $G$ is uniquely determined by its vector of distances to the chosen…

math.CO2014★ 6 cited

On Zero Forcing Number of Graphs and Their Complements

Linda Eroh, Cong X. Kang, Eunjeong Yi

The \emph{zero forcing number}, $Z (G)$ , of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V (G) ∖ S$ are colored white) such tha…

math.CO2014

A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs

Cong X. Kang, Eunjeong Yi

The \emph{zero forcing number}, $Z (G)$ , of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V (G) - S$ are colored white) such that $V (G)$ i…

math.CO2012★ 7 cited

Metric Dimension and Zero Forcing Number of Two Families of Line Graphs

Linda Eroh, Cong X. Kang, Eunjeong Yi

Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the "AIM Minimum Rank -- Special Graphs Work Group", where…

math.CO2012★ 1 cited

On Zero Forcing Number of Functigraphs

Cong X. Kang, Eunjeong Yi

\emph{Zero forcing number}, $Z (G)$ , of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V (G) ∖ S$ are colored white) such that $V…

math.CO2012★ 2 cited

Total Domination Value in Graphs

Cong X. Kang

A set $D \subseteq V (G)$ is a \emph{total dominating set} of $G$ if for every vertex $v \in V (G)$ there exists a vertex $u \in D$ such that $u$ and $v$ are adjacent. A total domina…

math.CO2012★ 17 cited

Probabilistic Zero Forcing in Graphs

Cong X. Kang, Eunjeong Yi

The \emph{zero forcing number} $Z (G)$ of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)\setminusS$ are colored white) such that $V…

math.CO2011★ 8 cited

On Metric Dimension of Functigraphs

Linda Eroh, Cong X. Kang, Eunjeong Yi

The \emph{metric dimension} of a graph $G$ , denoted by $dim (G)$ , is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vert…

math.CO2011★ 2 cited

Domination in Functigraphs

Linda Eroh, Ralucca Gera, Cong X. Kang +2

Let $G_{1}$ and $G_{2}$ be disjoint copies of a graph $G$ , and let $f : V (G_{1}) \to V (G_{2})$ be a function. Then a \emph{functigraph} $C (G, f) = (V, E)$ has the vertex set $V=V(G_1)…

math.CO2011★ 31 cited

Iteration Index of a Zero Forcing Set in a Graph

Kiran B. Chilakamarri, Nathaniel Dean, Cong X. Kang +1

Let each vertex of a graph G = (V(G), E(G)) be given one of two colors, say, "black" and "white". Let Z denote the (initial) set of black vertices of G. The color-change rule conve…

On Distance and Strong Metric Dimension of the Modular Product

Maker-Breaker Strong Resolving Game

Maker-Breaker Metric Resolving Games on Graphs

Distance-k locating-dominating sets in graphs

The Simultaneous Fractional Dimension of Graph Families

Maker-Breaker resolving game

On Laplacian Monopoles

The connected metric dimension at a vertex of a graph

The fractional k-metric dimension of graphs

The fractional strong metric dimension in three graph products

On Domination Number and Distance in Graphs

A Comparison between the Metric Dimension and Zero Forcing Number of Trees and Unicyclic Graphs

On Zero Forcing Number of Graphs and Their Complements

A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs

Metric Dimension and Zero Forcing Number of Two Families of Line Graphs

On Zero Forcing Number of Functigraphs

Total Domination Value in Graphs

Probabilistic Zero Forcing in Graphs

On Metric Dimension of Functigraphs

Domination in Functigraphs

Iteration Index of a Zero Forcing Set in a Graph

Distance- $k$ locating-dominating sets in graphs

The fractional $k$ -metric dimension of graphs