Local Metric Dimension of Some (k,6)-Fullerenes

Document Type : Research Paper

Authors

1 Department of Pure Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎Ferdowsi University of Mashhad‎, ‎P.O.\ Box 1159‎, ‎Mashhad 91775‎, ‎Iran

2 Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎Ferdowsi University of Mashhad‎, ‎P.O.\ Box 1159‎, ‎Mashhad 91775‎, ‎Iran

Abstract

A (k,6)-fullerene graph refers to a planar 3-connected cubic graph whose faces are k-gons and hexagons‎.
‎The current study involves calculating the local metric dimension for specific (k,6)-fullerene graphs‎, ‎where k takes values in the set {3‎, ‎4‎, ‎5}‎.

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Main Subjects

References

[1] T. Došlic, Cyclical edge-connectivity of fullerene graphs and (k; 6)-cages, J. Math. Chem. 33 (2003) 103–112, https://doi.org/10.1023/A:1023299815308.
[2] M. Arabzadeh, G. H. Fath-Tabar, H. Rasouli and A. Tehranian, On the difference between Laplacian and signless Laplacian coefficients of a graph and its applications on the fullerene graphs, Iranian J. Math. Chem. 15 (2024) 39–50,
https://doi.org/10.22052/IJMC.2024.254123.1808.
[3] S. Bakaein, M. Tavakoli, A. R. Ashrafi and O. Ori, Coloring of fullerenes, Fuller. Nanotub. Carbon Nanostructures 26 (2018) 705–708, https://doi.org/10.1080/1536383X.2018.1481049.
[4] P. Bonyabadi, K. Khashyarmanesh, M. Tavakoli and M. Afkhami, Edge metric dimension of fullerenes, Iranian J. Math. Chem. 14 (2023) 47–54, https://doi.org/10.22052/IJMC.2022.248392.1666.
[5] M. Faghani and E. Pourhadi, New expansion for certain isomers of various classes of fullerenes, Math. Interdisc. Res. 2 (2017) 33–43, https://doi.org/10.22052/MIR.2017.74726.1053.
[6] F. Koorepazan-Moftakhar, A. R. Ashrafi, O. Ori and M. V. Putz, Topological invariants of nanocones and fullerenes, Curr. Org. Chem. 19 (2015) 240–248, https://doi.org/10.2174/1385272819666141216230152.
[7] F. Koorepazan-Moftakhar, A. R. Ashrafi, Z. Mehranian and M. Ghorbani, Automorphism group and fixing number of (3; 6)- and (4; 6)-fullerene graphs, Electron. Notes Discret. Math 45 (2014) 113–120, https://doi.org/10.1016/j.endm.2013.11.022.
[8] P. Schwerdtfeger, L. Wirz and J. Avery, Program fullerene: a software package for constructing and analyzing structures of regular fullerenes, J. Comput. Chem. 34 (2013) 1508–1526, https://doi.org/10.1002/jcc.23278.
[9] M. Taheri-Dehkordi, Introducing two transformations in fullerene graphs, star and semi-star, Iranian J. Math. Chem. 14 (2023) 135–143, https://doi.org/10.22052/IJMC.2023.252986.1722.
[10] F. Okamoto, L. Crosse, B. Phinezy and P. Zhang, The local metric dimension of a graph, Math. Bohem. 135 (2010) 239–255.
[11] H. Fernau and J. A. Rodríguez-Velázquez, On the (adjacency) metric dimension of corona and strong product graphs and their local variants: combinatorial and computational results, Discrete Appl. Math. 236 (2018) 183–202, https://doi.org/10.1016/j.dam.2017.11.019.
[12] H. Fernau, J. A. Rodríguez-Velázquez and J. Alberto, Notions of metric dimension of corona products: combinatorial and computational results, in: Lecture Notes in Computer Science, vol. 8476, Springer, Cham, 2014, https://doi.org/10.1007/978-3-319-06686-8_12.
[13] S. Klavžar and M. Tavakoli, Local metric dimension of graphs: generalized hierarchical products and some applications, Appl. Math. Comput. 364 (2020) #124676, https://doi.org/10.1016/j.amc.2019.124676.
[14] J. A. Rodríguez-Velázquez, C. G. Gómez and G. A. Barragán-Ramírez, Computing the local metric dimension of a graph from the local metric dimension of primary subgraphs, Int. J. Comput. Math. 92 (2015) 686–693.
[15] J. A. Rodríguez-Velázquez, G. A. Barragán-Ramírez and C. G. Gómez, On the local metric dimension of corona product graphs, Bull. Malays. Math. Sci. Soc. 39 (2016) 157–173, https://doi.org/10.1007/s40840-015-0283-1.
[16] S. W. Saputro, On local metric dimension of (n - 3)-regular graph, J. Combin. Math. Combin. Comput. 98 (2016) 43–54.
[17] S. Akhter and R. Farooq, Metric dimension of fullerene graphs, Electron. J. Graph Theory Appl. (EJGTA) 7 (2019) 91–103, http://doi.org/10.5614/ejgta.2019.7.1.7.
 
Iranian Journal of Mathematical Chemistry
Volume 16, Issue 3
September 2025
Pages 171-179

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