‎‎Edge Metric Dimension of 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 Dep. of Math. Ferdowsi University of Mashhad

3 Ferdowsi University of Mashhad, I R Iran

4 Department of Mathematics‎, ‎University of Neyshabur, ‎P.O.Box 91136-899‎, ‎Neyshabur‎, ‎Iran

Abstract

‎A $(k,6)$-fullerene graph is a planar $3$-connected cubic graph whose faces are $k$-gons and hexagons‎. ‎The aim of this paper is to‎ study the edge metric dimension of $(3,6)$‎- ‎and $(4,6)$-fullerene graphs‎.

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Main Subjects


[1] P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Oxford University Press,
Oxford, 1995.
[2] T. Došlic, Cyclical edge-connectivity of fullerene graphs and (k; 6)-cages, cages. J. Math.
Chem. 33 (2003) 103–112, https://doi.org/10.1023/A:1023299815308.
[3] A. Kelenc, N. Tratnik and I. G. Yero, Uniquely identifying the edges of a
graph: The edge metric dimension, Discrete Appl. Math. 251 (2018) 204–220,
https://doi.org/10.1016/j.dam.2018.05.052.
[4] S. Klavžar and M. Tavakoli, Edge metric dimensions via hierarchical product and integer
linear programming, Optim. Lett. 15 (2021) 1993–2003, https://doi.org/10.1007/s11590-
020-01669-x.
[5] M. Afkhami, K. Khashyarmanesh and M. Tavakoli, L-clique metric dimension of graphs,
Bull. Malays. Math. Sci. Soc. 45 (2022) 2865–2883, https://doi.org/10.1007/s40840-022-
01299-9.
[6] R. Adawiyah, Dafik, R. Alfarisi, R. M. Prihandini and I. H. Agustin, Edge metric dimension
on some families of tree, J. Phys.: Conf. Ser. Series 1180 (2019) p. 012005,
https://doi.org/10.1088/1742-6596/1180/1/012005.
[7] V. Filipovic, A. Kartelj and J. Kratica, Edge metric dimension of some generalized petersen
graphs, Results Math. 74 (2019) p. 182, https://doi.org/10.1007/s00025-019-1105-9.
[8] B. Yang, M. Rafiullah, H. M. A. Siddiqui and S. Ahmad, On resolvability
parameters of some wheel-related graphs, J. Chem. (2019) Article ID 9259032,
https://doi.org/10.1155/2019/9259032.
[9] Y. Zhang and S. Gao, On the edge metric dimension of convex polytopes and its related
graphs, J. Comb. Optim. 39 (2020) 334–350, https://doi.org/10.1007/s10878-019-00472-4.
[10] S. Akhter and R. Farooq, Metric dimension of fullerene graphs, Electron. J. Graph Theory
Appl. 7 (1) (2019) 91–103, http://dx.doi.org/10.5614/ejgta.2019.7.1.7.