MANUSCRIPTS

Injective colorings of Sierpiński-like graphs and Kneser graphs. 2024. (with B. Brešar, S. Klavžar, B. Samadi)

The k-distance mutual-visibility problem in graphs. 2024.  (with M. Cera, P. García-Vázquez, J. C. Valenzuela-Tripodoro)

Coloring the vertices of a graph with mutual-visibility property. 2024. (with S. Klavžar, D. Kuziak, and J. C. Valenzuela Tripodoro)

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results. 2021. (with D. Kuziak)

IN PRESS

Lower general position sets in graphs. Discussiones Mathematicae Graph Theory.  In press since  2024. (with G. Di Stefano, S. Klavžar, A. Krishnakumar, and J. Tuite)

2025

Complexity issues concerning the quadruple Roman domination problem in graphs, Theoretical Computer Science  1026  (2025) article # 115013. (with V. S. R. Palagiri, G. P. Sharma) – (arxiv)

2024

A note on total co-independent domination in trees, Contributions to Discrete Mathematics 19(3) (2024) 184–195. (with A. Cabrera Martínez, F. A. Hernández Mira and J. M. Sigarreta Almira) – (arxiv)

On the total version of the covering Italian domination problem, Discrete Applied Mathematics  358 (2024) 333–343. (with S. A. Raju M. and V. S. R. Palagiri)

Mutual-visibility in strong products of graphs via total mutual-visibility, Discrete Applied Mathematics  358 (2024) 136–146. (with S. Cicerone, G. Di Stefano and S. Klavžar)

Mutual-visibility problems on graphs of diameter two, European Journal of Combinatorics  120 (2024) article # 103995. (with S. Cicerone, G. Di Stefano and S. Klavžar)

Complexity and equivalency of multiset dimension and ID-colorings,  Fundamenta Informaticae  191(3-4) (2024) 315–330. (with A. Hakanen) – (arxiv)

Resolving vertices of graphs with differences, Computational and Applied Mathematics  43  (2024) article # 275. (with I. Peterin, J. Sedlar and R. Škrekovski)

On the unicyclic graphs having vertices that belong to all their (strong) metric bases, Discrete Applied Mathematics  353 (2024) 191–207. (with A. Hakanen, V. Junnila and T. Laihonen)

Injective coloring of product graphs, Bulletin of the Malaysian Mathematical Sciences Society  47 (2024)  article # 86. (with B. Samadi and N. Soltankhah)

Resolvability and convexity properties in the Sierpiński product of graphs, Mediterranean Journal of Mathematics  21  (2024)  article # 3. (with M. A. Henning and S. Klavžar)

Lower (total) mutual visibility number in graphs, Applied Mathematics and Computation  465 (2024) article # 128411. (with B. Bresar)

2023

On the (k,l)-anonymity of networks via their k-metric antidimension, Scientific Reports  (Nature portfolio) 13 (2023) article # 19090.  (with E. Fernández, D. Kuziak and M. Muñoz-Márquez)

Traversing a graph in general position, Bulletin of the Australian Mathematical Society  108 (3) (2023) 353–365. (with S. Klavžar, A. Krishnakumar and J. Tuite)

On mixed metric dimension in subdivision, middle, and total graphs, Quaestiones Mathematicae  46 (12) 2023 2517–2527. (with A. Ghalavand, S. Klavžar and M. Tavakoli)

Variety of mutual-visibility problems in graphs, Theoretical Computer Science 974 (2023) article # 114096. (with S. Cicerone, G. Di Stefano, L. Drozdek, J. Hedzet and S. Klavžar)

The edge partition dimension of graphs, Discrete Mathematics Letters 12 (2023) 34–39. ( with D. Kuziak, E. Maritz and T. Vetrik)

Injective coloring of graphs revisited, Discrete Mathematics 346(5) (2023) article # 113348. (with B. Bresar and B. Samadi)

Further contributions on the outer multiset dimension of graphs, Results in Mathematics 78(2) (2023) article # 50. (with S. Klavžar and D. Kuziak)

On metric dimensions of hypercubes, Ars Mathematica Contemporanea 23(2) (2023) article # P2.08. (with A. Kelenc, A. T. Masa Toshi and R. Škrekovski)

Global offensive k-alliances in digraphs, Bulletin of the Institute of Combinatorics and its Applications 97 (2023) 67–82. (with D. A. Mojdeh and B. Samadi)

2022

On vertices contained in all or in no metric basis, Discrete Applied Mathematics 319 (2022) 407–423. (with A. Hakanen, V. Junnila and T. Laihonen)

A note on the metric and edge metric dimensions of 2-connected graphs, Discrete Applied Mathematics 319 (2022) 454–460. (with M. Knor and R. Škrekovski)

Relating the outer-independent total Roman domination number with some classical parameters of graphs, Mediterranean Journal of Mathematics 19(3) (2022)  article # 144. (with A. Cabrera Martínez and D. Kuziak)

Outer independent double Roman domination number of graphs, Bulletin of the Iranian Mathematical Society 48 (2022) 1789–1803 . (with D. A. Mojdeh, B. Samadi and Z. Shao)

On the total co-independent domination number of some graph operations, Revista de la Unión Matemática Argentina. 63(1) (2022) 153–168 . (with A. Cabrera Martínez, S. Cabrera García and I. Peterin)

Further results on packing related parameters in graphs, Discussiones Mathematicae Graph Theory 42(2) (2022) 333–348. (with D. A. Mojdeh and B. Samadi)

Incidence dimension and 2-packing number in graphs, RAIRO Operations Research  56(1)  (2022) 199–211. (with D. Bozovic, A. Kelenc and I. Peterin)

2021

A Steiner general position problem in graph theory, Computational and Applied Mathematics 40(6) (2021) article # 223. (with S. Klavžar, D. Kuziak and I. Peterin)

On the packing partitioning problem on directed graphs, Mathematics 9(23) (2021) article # 3148. (with B. Samadi)

Covering Italian domination in graphs, Discrete Applied Mathematics 304 (2021) 324–331. (with A. Khodkar, D. A. Mojdeh and B. Samadi)

General d-position sets, Ars Mathematica Contemporanea  21(1) (2021) article # P1.03. (with S. Klavžar and D. F. Rall)

Roman domination in direct product graphs and rooted product graphs, AIMS Mathematics 6(10) (2021) 11084–11096. (with A. Cabrera Martínez and I. Peterin)

On general position sets in Cartesian products, Results in Mathematics 76(3) (2021) article # 123.  (with S. Klavžar, B. Patkos and G. Rus)

Maker-Breaker resolving game, Bulletin of the Malaysian Mathematical Sciences Society  44 (4) (2021) 2081–2099. (with C. X. Kang, S. Klavžar and E. Yi)

On the (k,t)-metric dimension of graphs,The Computer Journal 64 (5) (2021) 707–720. (with A. Estrada-Moreno and J. A. Rodríguez-Velázquez)

On the total and strong version for Roman dominating functions in graphs, Aequationes Mathematicae 95 (2021) 215–236. (with S. Nazari-Moghaddam, M. Soroudi and S.M. Sheikholeslami)

Total Roman {2}-domination in graphs, Quaestiones Mathematicae  44(3) (2021) 411–434. (with S. Cabrera García, A. Cabrera Martínez and F. A. Hernández Mira)

Graphs with the edge metric dimension smaller than the metric dimension, Applied Mathematics and Computation 401 (2021) article # 126076. (with M. Knor, S. Majstorovic, A. T. Masa Toshi and R. Škrekovski)

On three outer-independent domination related parameters in graphs, Discrete Applied Mathematics 294 (2021) 115–124. (with D. A. Mojdeh, I. Peterin and B. Samadi)

A constructive characterization of vertex cover Roman trees, Discussiones Mathematicae Graph Theory  41 (2021) 267–283.  (with A. Cabrera Martínez and D. Kuziak)

Independent transversal total domination versus total domination in trees, Discussiones Mathematicae Graph Theory  41 (2021) 213–224. (with A. Cabrera Martínez and I. Peterin)

2020

(Open) packing number of some graph products, Discrete Mathematics & Theoretical Computer Science  22(4) (2020), article # 1. (with D. A. Mojdeh, I. Peterin and B. Samadi)

Dominating the direct product of two graphs through total Roman strategies, Mathematics (MDPI) 8(9) (2020), article # 1438. (with A. Cabrera Martinez, D. Kuziak and I. Peterin)

Constructive characterizations concerning weak Roman domination in trees, Discrete Applied Mathematics 284 (2020) 384–390. (with A. Cabrera Martínez)

Global defensive k-alliances in directed graphs: combinatorial and computational issues, RAIRO – Operations Research 54 (4) (2020) 1027–1040. (with D. A. Mojdeh and B. Samadi)

Further new results on strong resolving partitions for graphs, Open Mathematics 18(1) (2020) 237–248. (with D. Kuziak)

Edge metric dimension of some graph operations, Bulletin of the Malaysian Mathematical Sciences Society   43 (2020) 2465–2477. (with I. Peterin)

The simultaneous strong resolving graph and the simultaneous strong metric dimension of graph families, Mathematics  (MDPI) 8 (1) (2020), article # 125. (single author)

2019

Packing and domination parameters in digraphs, Discrete Applied Mathematics 269 (2019) 184–192. (with D. A. Mojdeh and B. Samadi)

Outer-independent total Roman domination in graphs, Discrete Applied Mathematics 269 (2019) 107–119. (with A. Cabrera Martínez and D. Kuziak)

The general position problem and strong resolving graphs, Open Mathematics  17(1) (2019) 1126–1135. (with S. Klavžar)

Quasi-total Roman domination in graphs, Results in Mathematics 74 (2019), article # 173. (with S. Cabrera-García and A. Cabrera-Martínez)

Distance-based vertex identification in graphs: the outer multiset dimension, Applied Mathematics and Computation 363 (2019),  article #124612. (with R. Gil-Pons, Y. Ramírez-Cruz and R. Trujillo-Rasúa)

Efficient closed domination in digraph products, Journal of Combinatorial Optimization 38 (1) (2019) 130–149. (with I. Peterin)

A characterization of trees with equal Roman 2-domination and Roman domination numbers, Communications in Combinatorics and Optimization 4 (2) (2019) 95–107. (with A. Cabrera Martínez)

On the computational complexities of three problems related to a privacy measure for large networks under active attack, Theoretical Computer Science  775  (2019) 53–67. (with T. Chatterjee, B. DasGupta, N, Mobasheri and V. Srinivasan)

The fractional k-metric dimension of graphs, Applicable Analysis and Discrete Mathematics 13 (2019) 203–223. (with C. X. Kang and E. Yi)

On computational and combinatorial properties of the total co-independent domination number of graphs, The Computer Journal 62 (1) (2019) 97–108. (with A. Cabrera Martínez, F. A. Hernández Mira and J. M. Sigarreta Almira)

Error-correcting codes from k-resolving sets, Discussiones Mathematicae Graph Theory 39 (2) (2019) 341–355. (with R. F. Bailey)

On analyzing and evaluating privacy measures for social networks under active attack, Information Sciences 473 (2019) 87–100. (with B. DasGupta and N. Mobasheri)

2018

Uniquely identifying the edges of a graph: the edge metric dimension, Discrete Applied Mathematics 251 (2018) 204–220. (with A. Kelenc and N. Tratnik)

The fractional strong metric dimension in three graph products, Discrete Applied Mathematics 251 (2018) 190–203. (with C. X. Kang and E. Yi)

Strong resolving graphs: the realization and the characterization problems, Discrete Applied Mathematics 236 (2018) 270–287. (with D. Kuziak, M. L. Puertas and J. A. Rodríguez-Velázquez)

Bounding the open k-monopoly number of strong product graphs, Discussiones Mathematicae Graph Theory 38 (2018) 287–299. (with D. Kuziak and I. Peterin)

2017

A survey on alliances in graphs: defensive alliances, Utilitas Mathematica 105 (2017) 141–172. (with J. A. Rodríguez-Velázquez)

On the strong Roman domination number of graphs, Discrete Applied Mathematics 231 (2017) 44–59. (with M. P. Alvarez-Ruiz, T. Mediavilla-Gradolph, S. M. Sheikholeslami and J. C. Valenzuela)

The forcing total restrained geodetic number and the total restrained geodetic number of a graph: realizability and complexity, AKCE International Journal of Graphs and Combinatorics 14 (3) (2017) 242–250. (with H. Abdollahzadeh Ahangar, M. Najimi, V. Samodivkin)

Mixed metric dimension of graphs, Applied Mathematics and Computation 314 (2017) 429–438. (with A. Kelenc, D. Kuziak and A. Taranenko)

On the independence transversal total domination number of graphs, Discrete Applied Mathematics 219 (2017) 65–73. (with A. Cabrera Martínez and J. M. Sigarreta)

On some resolving partitions for the lexicographic product of two graphs, International Journal of Computer Mathematics 94 (7) (2017) 1363–1374. (with N. Campanelli)

Computing the k-metric dimension of graphs, Applied Mathematics and Computation 300 (2017) 60–69. (with A. Estrada-Moreno and J. A. Rodríguez-Velázquez) – There is a significant gap in the NP-completeness reduction made in the work. There has appeared a correction for it here.

On global (strong) defensive alliances in some product graphs, Communications in Combinatorics and Optimization 2 (1) (2017) 21–33. (with M. Jakovac and D. Kuziak)

Graphs that are simultaneously efficient open domination and efficient closed domination graphs, Discrete Applied Mathematics 217 (Part 3) (2017) 613–621. (with S. Klavzar and I. Peterin)

Resolvability and strong resolvability in the direct product of graphs, Results in Mathematics 71 (1) (2017) 509–526. (with D. Kuziak and I. Peterin)

Computing the metric dimension of a graph from primary subgraphs, Discussiones Mathematicae Graph Theory 37 (1) (2017) 273–293. (with D. Kuziak and J. A. Rodríguez-Velázquez)

2016

Vertices, edges, distances and metric dimension in graphs, Electronic Notes in Discrete Mathematics 55 (2016) 191–194. (single author)

Total Roman domination in graphs, Applicable Analysis and Discrete Mathematics 10 (2016) 501–517. (with H. Abdollahzadeh Ahangar, M. A. Henning and V. Samodivkin)

Relationships between the 2-metric dimension and the 2-adjacency dimension in the lexicographic product of graphs, Graphs and Combinatorics 32 (6) (2016) 2367–2392. (with A. Estrada-Moreno and J. A. Rodríguez-Velázquez)

The security number of strong grid-like graphs, Theoretical Computer Science 653 (2016) 1–14. (with M. Jakovac and D. Kuziak)

Convex dominating-geodetic partitions in graphs, FILOMAT 30 (11) (2016) 3075–3082. (with M. Lemanska)

Closed formulae for the strong metric dimension of lexicographic product graphs, Discussiones Mathematicae Graph Theory 36 (4) (2016) 1051–1064. (with D. Kuziak and J. A. Rodríguez-Velázquez)

On the monopolies of lexicographic product graphs: bounds and closed formulaes, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie 59 (4) (2016) 355–366. (with D. Kuziak and I. Peterin)

Characterizing 1-metric antidimensional trees and unicyclic graphs, The Computer Journal 59 (8) (2016) 1264–1273. (with R. Trujillo-Rasúa)

The partition dimension of corona product graphs, Ars Combinatoria 127 (2016) 387–399. (with D. Kuziak and J. A. Rodríguez-Velázquez)

The k-metric dimension of the lexicographic product of graphs, Discrete Mathematics 339 (7) (2016) 1924–1934. (with A. Estrada-Moreno and J. A. Rodríguez-Velázquez)

Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs, Opuscula Mathematica 36 (5) (2016) 575–588. (with M. Dettlaff and J. Raczek)

The k-metric dimension of corona product graphs, Bulletin of the Malaysian Mathematical Sciences Society 39 (2016) 135–156. (Special Issue on Graph Theory). (with A. Estrada-Moreno and J. A. Rodríguez-Velázquez)

Open k-monopolies in graphs: complexity and related concepts, Discrete Mathematics & Theoretical Computer Science 18 (3) (2016) #3. (with D. Kuziak and I. Peterin)

Strong metric dimension of rooted product graphs, International Journal of Computer Mathematics, 93 (8) (2016) 1265–1280. (with D. Kuziak and J. A. Rodríguez-Velázquez)

Strong resolving partitions for strong product graphs and Cartesian product graphs, Discrete Applied Mathematics 202 (2016) 70–78. (single author)

k-metric antidimension: a privacy measure for social graphs, Information Sciences 328 (2016) 403–417. (with R. Trujillo-Rasúa)

Independent transversal dominating sets in graphs: complexity and structural properties, FILOMAT 30 (2) (2016) 293–303. (with H. Abdollahzadeh Ahangar and V. Samodivkin)

Domination related parameters in rooted product graphs, Bulletin of the Malaysian Mathematical Sciences Society 39 (1) (2016) 199–217. (with D. Kuziak and M. Lemanska)

2015

Analogies between the geodetic number and the Steiner number of some classes of graphs, FILOMAT 29 (8) (2015) 1781–1788. (with J. A. Rodríguez-Velázquez)

On the strong metric dimension of Cartesian sum graphs, Fundamenta Informaticae 141 (2015) 57–69. (with D. Kuziak and J. A. Rodríguez-Velázquez)

The k-metric dimension of a graph, Applied Mathematics & Information Sciences 9 (6) (2015) 2829–2840. (with A. Estrada-Moreno and J. A. Rodríguez-Velázquez)

Computing the (k-)monopoly number of direct product of graphs, FILOMAT 29 (5) (2015) 1163–1171. (with D. Kuziak and I. Peterin)

The metric dimension of strong product graphs, Carpathian Journal of Mathematics 31 (2) (2015) 261–268. (with J. A. Rodríguez-Velázquez, D. Kuziak and J. M. Sigarreta)

Partial product of graphs and Vizing’s conjecture, Ars Mathematica Contemporanea 9 (2015) 19–25. (single author)

On the strong metric dimension of the strong products of graphs, Open Mathematics (formerly Central European Journal of Mathematics) 13 (2015) 64–74. (with D. Kuziak  and J. A. Rodríguez-Velázquez)

Erratum to “On the strong metric dimension of the strong products of graphs, Open Mathematics 13 (2015) 64–74″, Open Mathematics (formerly Central European Journal of Mathematics) 13 (2015) 209-210. (with D. Kuziak  and J. A. Rodríguez-Velázquez)

2014

On the partition dimension of unicyclic graphs, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie 57 (4) (2014) 381–391.  (with J. A. Rodríguez-Velázquez and H. Fernau)

On the strong partition dimension of graphs, The Electronic Journal of Combinatorics 21 (3)  (2014)  # P3.14. (single author)

On the strong metric dimension of Cartesian and direct products of graphs, Discrete Mathematics 335 (2014) 8–19. (with J. A. Rodríguez-Velázquez, D. Kuziak and O. R. Oellermann)

The partition dimension of strong product graphs and Cartesian product graphs, Discrete Mathematics 331 (2014) 43–52.  (with M. Jakovac, D. Kuziak and A. Taranenko)

k-metric resolvability in graphs, Electronic Notes in Discrete Mathematics 46 (2014) 121–128. (with A. Estrada-Moreno and J. A. Rodríguez-Velázquez)

On the strong metric dimension of product graphs, Electronic Notes in Discrete Mathematics 46 (2014) 169–176. (with J. A. Rodríguez-Velázquez and D. Kuziak)

Erratum to “Total domination number of cartesian products” [Math. Commun. 9 (2004) 35-44], Mathematical Communications 19 (2014) 195–200. (with D. Kuziak and I. Peterin)

Efficient open domination in graph products, Discrete Mathematics and Theoretical Computer Science 16 (1) (2014) 105–120. (with D. Kuziak and I. Peterin)

Bondage number of grid graphs, Discrete Applied Mathematics 167 (2014) 94–99. (with M. Dettlaff and M. Lemanska)

On the partition dimension of trees, Discrete Applied Mathematics 166 (2014) 204–209. (with M. Lemanska and J. A. Rodríguez-Velázquez)

2013

Corrections to the article “The metric dimension of graph with pendant edges” [JCMCC, 65 (2008) 139-145], Journal of Combinatorial Mathematics and Combinatorial Computing 87 (2013) 43–50. (with D. Kuziak and J. A. Rodríguez-Velázquez)

Roman domination in Cartesian product graphs and strong product graphs, Applicable Analysis and Discrete Mathematics 7 (2013) 262–274. (with J. A. Rodríguez-Velázquez)

Coloring, location and domination of corona graphs, Aequationes Mathematicae 86 (2013) 1–21. (with D. Kuziak and A. Rondón Aguilar)

Boundary powerful k-alliances in graphs, Ars Combinatoria 111 (2013) 495–504. (with J. A. Rodríguez-Velázquez) (Accepted since 2009)

Alliance free in Cartesian product graphs, Discrete Applied Mathematics 161 (10–11) (2013) 1618-1625. (with S. Bermudo and J. A. Rodríguez-Velázquez)

On Clark & Suen bound type results for k-domination and Roman domination of Cartesian product graphs, International Journal of Computer Mathematics 90 (3) (2013) 522–526. (single author)

On the strong metric dimension of corona product graphs and join graphs, Discrete Applied Mathematics 161 (7-8) (2013) 1022–1027. (with D. Kuziak and J. A. Rodríguez-Velázquez)

Computing global offensive alliances in Cartesian product graphs, Discrete Applied Mathematics 161 (2013) 284–293. (with J. A. Rodríguez-Velázquez)

2012

Nordhaus-Gaddum results for the convex domination number, Periodica Mathematica Hungarica 65 (1) (2012) 125–134. (with M. Lemanska and J. A. Rodríguez-Velázquez)

The limit case of a domination property, Acta Mathematica Sinica-English Series 28 (3) (2012) 463–468. (with M. Lemanska and J. A. Rodríguez-Velázquez)

Partitioning a graph into global powerful k-alliances, Graphs and Combinatorics 28 (2012) 575–583. (with J. A. Rodríguez-Velázquez)

2011

On the metric dimension of corona product graphs, Computers & Mathematics with Applications 61 (9) (2011) 2793–2798. (with D. Kuziak and J. A. Rodríguez-Velázquez)

Alliance free and alliance cover sets, Acta Mathematica Sinica-English Series 27 (3) (2011) 497–504. (with S. Bermudo, J. A. Rodríguez-Velázquez and J. M. Sigarreta)

Partitioning a graph into defensive k-alliances, Acta Mathematica Sinica-English Series 27 (1) (2011) 73–82. (with S. Bermudo, J. A. Rodríguez-Velázquez and J. M. Sigarreta)

Partitioning a graph into offensive k-alliances, Discrete Applied Mathematics 159 (2011) 224–231. (with S. Bermudo, J. A. Rodríguez-Velázquez and J. M. Sigarreta)

2010

A note on the partition dimension of Cartesian product graphs, Applied Mathematics and Computation 217 (7) (2010) 3571–3574. (with J. A. Rodríguez-Velázquez)

Estimating the higher-order Randic index, Chemical Physics Letters 489 (1-3) (2010) 118–120. (with I. Gutman and J. A. Rodríguez-Velázquez)

On global offensive k-alliances in graphs, Applied Mathematics Letters 23 (12) (2010) 1454–1458. (with S. Bermudo, J. A. Rodríguez-Velázquez and J. M. Sigarreta)

On geodetic and k-geodetic sets in graphs, Ars Combinatoria 96 (2010) 469–478. (with S. Bermudo, J. A. Rodríguez-Velázquez and J. M. Sigarreta)

Boundary defensive k-alliances in graphs, Discrete Applied Mathematics 158 (11) (2010) 1205–1211. (with J. A. Rodríguez-Velázquez)

2009

Defensive k-alliances in graphs, Applied Mathematics Letters 22 (1) (2009) 96–100. (with J. A. Rodríguez-Velázquez and J. M. Sigarreta)