D. Kuziak

activity

20102026

most citedOn the metric dimension of corona product graphs

149 citations · 294 across the 29 of their papers we have counts for

collaborators

34 papers

physics.soc-ph2026

Vertices that belong to every minimum dominating set of a graph and their connection with transportation sharing systems with study cases in Campo de Gibraltar area

Mohammad Farhan, Dorota Kuziak, Iztok Peterin +1

This study addresses a theoretical model regarding equity and accessibility challenges in designing shared transportation systems (such as micro-mobility networks) by applying grap…

math.CO2026

A variety of the mutual-visibility coloring problem for graphs

Saneesh Babu, Marko Jakovac, Dorota Kuziak +2

This paper explores variations of vertex-coloring problems defined on graph visibility properties. It introduces and studies the dual, outer, and total mutual-visibility chromatic…

math.CO2026

Multiset resolvability parameters in graphs: A survey with new results and open problems

Mohammad Farhan, Sandi Klavžar, Dorota Kuziak +1

The metric dimension, which has lots of variants and numerous applications in other fields, is one of the most important and most extensively studied topics in metric graph theory.…

math.CO2026

The weak $k$ -metric dimension of the direct product of complete graphs

Mohammad Farhan, Dorota Kuziak, Ismael G. Yero

The weak $k$ -metric dimension of a graph is roughly understood as the cardinality of a smallest set of vertices $S$ of the graph with the property of uniquely recognizing all the v…

math.CO2025

On the $(k, ℓ)$ -multiset anonymity measure for social graphs

Alejandro Estrada-Moreno, Elena Fernández, Dorota Kuziak +3

The publication of social graphs must be preceded by a rigorous analysis of privacy threats against social graph users. When the threat comes from inside the social network itself,…

math.CO2025

On the weak $k$ -metric dimension of Hamming graphs

Elena Fernandez, Sandi Klavzar, Dorota Kuziak +2

Given a connected graph $G$ , a set of vertices $X \subset V (G)$ is a weak $k$ -resolving set of $G$ if for each two vertices $y, z \in V (G)$ , the sum of the values $|d_G(y,x)-d_G(z,x)|…

math.CO2025

Moving through Cartesian products, coronas and joins in general position

Sandi Klavžar, Aditi Krishnakumar, Dorota Kuziak +3

The general position problem asks for large sets of vertices such that no three vertices of the set lie on a common shortest path. Recently a dynamic version of this problem was de…

math.CO2024★ 1 cited

General position problems in strong and lexicographic products of graphs

Pakanun Dokyeesun, Sandi Klavžar, Dorota Kuziak +1

Outer, dual, and total general position sets are studied on strong and lexicographic products of graphs. Sharp lower and upper bounds are proved for the outer and the dual general…

math.CO2024

Coloring the vertices of a graph with mutual-visibility property

Sandi Klavžar, Dorota Kuziak, Juan Carlos Valenzuela Tripodoro +1

Given a graph $G$ , a mutual-visibility coloring of $G$ is introduced as follows. We color two vertices $x, y \in V (G)$ with a same color, if there is a shortest $x, y$ -path whose inte…

math.CO2024★ 1 cited

Maker-Breaker resolving game played on corona products of graphs

Tijo James, Sandi Klavžar, Dorota Kuziak +2

The Maker-Breaker resolving game is a game played on a graph $G$ by Resolver and Spoiler. The players taking turns alternately in which each player selects a not yet played vertex…

math.CO2023

Total mutual-visibility in graphs with emphasis on lexicographic and Cartesian products

Dorota Kuziak, Juan A. Rodríguez-Velázquez

Given a connected graph $G$ , the total mutual-visibility number of $G$ , denoted $μ_{t} (G)$ , is the cardinality of a largest set $S \subseteq V (G)$ such that for every pair of vertices…

math.CO2022

Nonlocal metric dimension of graphs

Sandi Klavžar, Dorota Kuziak

Nonlocal metric dimension $dim_{n ℓ} (G)$ of a graph $G$ is introduced as the cardinality of a smallest nonlocal resolving set, that is, a set of vertices which resolves…

math.CO2022

Further contributions on the outer multiset dimension of graphs

Sandi Klavzar, Dorota Kuziak, Ismael G. Yero

The outer multiset dimension $dim_{ms} (G)$ of a graph $G$ is the cardinality of a smallest set of vertices that uniquely recognize all the vertices outside this set by us…

math.CO2021

Relating the outer-independent total Roman domination number with some classical parameters of graphs

Abel Cabrera Martínez, Dorota Kuziak, Ismael G. Yero

For a given graph $G$ without isolated vertex we consider a function $f : V (G) \to {0, 1, 2}$ . For every $i \in {0, 1, 2}$ , let $V_{i} = {v \in V (G) : f (v) = i}$ . The function $f…

math.CO2021★ 19 cited

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Dorota Kuziak, Ismael G. Yero

Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an att…

math.CO2021

A Steiner general position problem in graph theory

Sandi Klavžar, Dorota Kuziak, Iztok Peterin +1

Let $G$ be a graph. The Steiner distance of $W \subseteq V (G)$ is the minimum size of a connected subgraph of $G$ containing $W$ . Such a subgraph is necessarily a tree called a Stei…

math.CO2020

Dominating the direct product of two graphs through total Roman strategies

Abel Cabrera Martinez, Dorota Kuziak, Iztok Peterin +1

Given a graph $G$ without isolated vertices, a total Roman dominating function for $G$ is a function $f : V (G) \to {0, 1, 2}$ such that every vertex with label 0 is adjacent…

math.CO2016★ 1 cited

Strong resolving graphs: the realization and the characterization problems

D. Kuziak, M. L. Puertas, J. A. Rodriguez-Velazquez +1

The strong resolving graph $G_{S R}$ of a connected graph $G$ was introduced in [Discrete Applied Mathematics 155 (1) (2007) 356--364] as a tool to study the strong metric dimension…

math.CO2016

Mixed metric dimension of graphs

Aleksander Kelenc, Dorota Kuziak, Andrej Taranenko +1

Let $G = (V, E)$ be a connected graph. A vertex $w \in V$ distinguishes two elements (vertices or edges) $x, y \in E \cup V$ if $d_{G} (w, x) \neq = d_{G} (w, y)$ . A set $S$ of vertices in a connecte…

math.CO2015★ 8 cited

On the strong metric dimension of Cartesian sum graphs

Dorota Kuziak, Ismael G. Yero, Juan A. Rodríguez-Velázquez

A vertex $w$ of a connected graph $G$ strongly resolves two vertices $u, v \in V (G)$ , if there exists some shortest $u - w$ path containing $v$ or some shortest $v - w$ path containing $…

math.CO2015

Resolvability and Strong Resolvability in the Direct Product of Graphs

Dorota Kuziak, Iztok Peterin, Ismael G. Yero

Given a connected graph $G$ , a vertex $w \in V (G)$ distinguishes two different vertices $u, v$ of $G$ if the distances between $w$ and $u$ and between $w$ and $v$ are different. More…

math.CO2015★ 5 cited

Open k-monopolies in graphs: complexity and related concepts

Dorota Kuziak, Iztok Peterin, Ismael G. Yero

Closed monopolies in graphs have a quite long range of applications in several problems related to overcoming failures, since they frequently have some common approaches around the…

math.CO2014

Closed formulae for the strong metric dimension of lexicographic product graphs

Dorota Kuziak, Ismael G. Yero, Juan A. Rodriguez-Velazquez

Given a connected graph $G$ , a vertex $w \in V (G)$ strongly resolves two vertices $u, v \in V (G)$ if there exists some shortest $u - w$ path containing $v$ or some shortest $v - w$ path c…

math.CO2013★ 1 cited

Strong metric dimension of rooted product graphs

Dorota Kuziak, Ismael G. Yero, Juan A. Rodríguez-Velázquez

Let $G$ be a connected graph. A vertex $w$ strongly resolves a pair $u$ , $v$ of vertices of $G$ if there exists some shortest $u - w$ path containing $v$ or some shortest $v - w$ path…

Vertices that belong to every minimum dominating set of a graph and their connection with transportation sharing systems with study cases in Campo de Gibraltar area

A variety of the mutual-visibility coloring problem for graphs

Multiset resolvability parameters in graphs: A survey with new results and open problems

The weak k-metric dimension of the direct product of complete graphs

On the (k,ℓ)-multiset anonymity measure for social graphs

On the weak k-metric dimension of Hamming graphs

Moving through Cartesian products, coronas and joins in general position

General position problems in strong and lexicographic products of graphs

Coloring the vertices of a graph with mutual-visibility property

Maker-Breaker resolving game played on corona products of graphs

Total mutual-visibility in graphs with emphasis on lexicographic and Cartesian products

Nonlocal metric dimension of graphs

Further contributions on the outer multiset dimension of graphs

Relating the outer-independent total Roman domination number with some classical parameters of graphs

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

A Steiner general position problem in graph theory

Dominating the direct product of two graphs through total Roman strategies

Strong resolving graphs: the realization and the characterization problems

Mixed metric dimension of graphs

On the strong metric dimension of Cartesian sum graphs

Resolvability and Strong Resolvability in the Direct Product of Graphs

Open k-monopolies in graphs: complexity and related concepts

Closed formulae for the strong metric dimension of lexicographic product graphs

Strong metric dimension of rooted product graphs

The weak $k$ -metric dimension of the direct product of complete graphs

On the $(k, ℓ)$ -multiset anonymity measure for social graphs

On the weak $k$ -metric dimension of Hamming graphs