On edge metric dimension of chemical chains
Beenish Amjadbeeniamjad57@gmail.comDepartment of MathematicsRawalpindi Women UniversityRawalpindi, 46000, Pakistan0009-0001-5006-0269View full profile → , Sarah Abdul Hameedsaraha.alkhafaji@uokufa.edu.iqDepartment of MathematicsFaculty of Computer Science and MathematicsUniversity of KufaNajaf, 540011, Iraq0009-0008-1873-4252View full profile → , Abdulkhaleq Husham Yousifabdulkhaleq.h.yousif@aliraqia.edu.iqDepartment of MathematicsResearch and Studies CenterIraqi UniversityBaghdad, 10071, Iraq0000-0002-8028-989XView full profile → , Deeba Afzaldeeba.afzal@f.rwu.edu.pkDepartment of MathematicsRawalpindi Women UniversityRawalpindi, 46000, Pakistan0000-0001-5268-7260View full profile → , Saima Mustafasaima.mustafa@f.rwu.edu.pkDepartment of MathematicsRawalpindi Women UniversityRawalpindi, 46000, Pakistan0000-0002-0584-1445View full profile → , Mohammad Reza Farahanimohammad_farahani@mathdep.iust.ac.irSchool of Mathematics and Computer ScienceIran University of Science and Technology (IUST)Narmak, Tehran, 16844, Iran0000-0003-2969-4280View full profile → , *Mehdi AlaeiyanCorresponding authoralaeiyan@iust.ac.irDepartment of Mathematics and Computer ScienceIran University of Science and Technology (IUST)Narmak, Tehran, 16844, Iran0000-0003-2185-5967View full profile → , Murat Cancanmcancan@yyu.edu.trDepartment of MathematicsFaculty of EducationYuzuncu Yil UniversityVan, 65090, Turkey0000-0002-8606-2274View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Mar 2025
- Published Online:
- 04 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2299
- Pages:
- 1–12
Abstract
The fundamentals of edge metric dimension are examined in this study, along with constraints for various graph types and algorithms for quickly computing edge-resolving sets. The EMD of a graph is an uniqueness of the metric dimension, which originated from the graph’s emphasis on vertex resolving sets. In this context, an edge-resolving set is a collection of vertices in which each edge of the graph can be particularly recognized by its distance from the vertices. In fields where edges must be found, such as network topology, robotic mobility, chemistry and combinatorial optimization, it is crucial.
Keywords
Subject Classifications
References
[1] A. Kelenc, N. Tratnik, and I. G. Yero, “Uniquely identifying the edges of a graph: The edge metric dimension,” Discrete Appl. Math., vol. 251, pp. 204–220 (2018), doi: 10.1016/j.dam.2018.05.052.
[2] A. G. Algam and H. B. Shelash, “Dynamics of monad graph of finite group,” J. Discrete Math. Sci. Cryptogr., vol. 24, no. 6, pp. 1589–1593 (2021), doi: 10.1080/09720529.2020.1790735.
[3] I. G. Yero, “Vertices, edges, distances and metric dimension in graphs,” Electron. Notes Discrete Math., vol. 55, pp. 191–194 (2016), doi: 10.1016/j.endm.2016.10.047.
[4] H. R. Hashim, F. Luca, H. B. Shelash, and A. A. Shukur, “Generalized Lucas graphs,” Afr. Mat., vol. 34, no. 1 (2023), doi: 10.1007/s13370-023-01048-6.
[5] R. Adawiyah, D. R. Alfarisi, R. M. Prihandini, and I. H. Agustin, “Edge metric dimension on some families of tree,” J. Phys. Conf. Ser., vol. 1180, Art. no. 012005 (2019), doi: 10.1088/1742-6596/1180/1/012005.
[6] R. Nasir, Z. Zahid, and S. Zafar, “Edge version of metric dimension for the families of grid graphs and generalized prism graphs,” Discrete Math. Algorithms Appl., vol. 12, no. 3, Art. no. 2050037 (2020), doi: 10.1142/S1793830920500378.
[7] M. Ahsan, Z. Zahid, S. Zafar, A. Rafiq, M. S. Sindhu, and M. Umar, “Computing the edge metric dimension of convex polytopes related graphs,” J. Math. Comput. Sci., vol. 22, no. 2, pp. 174–188 (2021), doi: 10.22436/jmcs.022.02.08.
[8] A. Ahmad, S. Husain, M. Azeem, K. Elahi, and M. K. Siddiqui, “Computation of edge resolvability of benzenoid tripod structure,” J. Math., vol. 2021, Art. no. 9336540 (2021), doi: 10.1155/2021/9336540.
[9] Z. Beerliova, E. Eberhard, T. Erlebach, A. Hall, M. Hoffmann, M. Mihalák, and L. S. Ram, “Network discovery and verification,” IEEE J. Sel. Areas Commun., vol. 24, no. 12, pp. 2168–2181 (2006), doi: 10.1109/JSAC.2006.884015.
[10] S. Khuller, B. Raghavachari, and A. Rosenfeld, “Landmarks in graphs,” Discrete Appl. Math., vol. 70, no. 3, pp. 217–229 (1996), doi: 10.1016/0166-218X(95)00106-2.
[11] R. A. Melter and I. Tomescu, “Metric bases in digital geometry,” Comput. Vis. Graph. Image Process., vol. 25, no. 1, pp. 113–121 (1984), doi: 10.1016/0734-189X(84)90051-3.
[12] D. Kuziak, “The strong resolving graph and the strong metric dimension of cactus graphs,” Mathematics, vol. 8, no. 8, Art. no. 1266 (2020), doi: 10.3390/math8081266.
[13] Z. Ahmad, M. A. Chaudhary, A. Q. Baig, and M. A. Zahid, “On metric dimension of P(n,2)∗K1 graph,” J. Discrete Math. Sci. Cryptogr., vol. 24, no. 2, pp. 629–645 (2021), doi: 10.1080/09720529.2021.1907017.
[14] Z. Ahmad, M. A. Chaudhary, A. Q. Baig, and M. A. Zahid, “Fault-tolerant metric dimension of P(n,2)∗K1 graph,” J. Discrete Math. Sci. Cryptogr., vol. 24, no. 2, pp. 647–656 (2021), doi: 10.1080/09720529.2021.1899209.
[15] S. Hameed, M. N. Husin, F. Afzal, H. Hussain, D. Afzal, M. R. Farahani, and M. Cancan, “On computation of newly defined degree-based topological invariants of bismuth tri-iodide via M-polynomial,” J. Discrete Math. Sci. Cryptogr., vol. 24, no. 7, pp. 2073–2091 (2021), doi: 10.1080/09720529.2021.1972615.
[16] F. Chaudhry, I. Shoukat, D. Afzal, C. Park, M. Cancan, and M. R. Farahani, “M-polynomials and degree-based topological indices of the molecule copper(I) oxide,” J. Chem., vol. 2021, Art. no. 6679819 (2021), doi: 10.1155/2021/6679819.
[17] M. Alaeiyan, “Characteristics and eigenvalues of the newly defined Ala graph,” Phys. Scr., vol. 100, no. 5, Art. no. 055201 (2025), doi: 10.1088/1402-4896/adc3d2.
[18] M. Imran, M. R. Farahani, M. Cancan, M. Alaeiyan, and A. Akgül, “On topological indices of certain families of graphs,” Phys. Scr., vol. 100, Art. no. 015208 (2025), doi: 10.1088/1402-4896/ad9065.




