
AIMS Mathematics, 2020, 5(6): 62216232. doi: 10.3934/math.2020400.
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
On the metric basis in wheels with consecutive missing spokes
1 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
2 Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
3 Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Received: , Accepted: , Published:
Keywords: metric dimension; basis; resolving set; wheel; missing spokes; exchange property
Citation: Syed Ahtsham Ul Haq Bokhary, ZilleShams, Abdul Ghaffar, Kottakkaran Sooppy Nisar. On the metric basis in wheels with consecutive missing spokes. AIMS Mathematics, 2020, 5(6): 62216232. doi: 10.3934/math.2020400
References:
 1. G. Abbas, U. Ali, M. Munir, et al. Power graphs and exchange property for resolving sets, Open Math., 17 (2019), 13031309.
 2. D. L. Boutin, Determining sets, resolving sets and the exchange property, Graphs Combin., 25 (2009), 789806.
 3. P. S. Buczkowski, G. Chartrand, C. Poisson, et al. On kdimensional graphs and their bases, Periodica Math. Hung., 46 (2003), 915.
 4. J. Caceres, C. Hernando, M. Mora, et al. On the metric dimension of cartesian product of graphs, SIAM J. Disc. Math., 2 (2007), 423441.
 5. P. J. Cameron, J. H. Van Lint, Designs, Graphs, Codes and their Links, London Mathematical Society Student Texts 22, Cambridge University Press, Cambridge, 1991.
 6. G. Chartrand, L. Eroh, M. A. Johnson, et al. Resolvability in graphs and metric dimension of a graph, Disc. Appl. Math., 105 (2000), 99113.
 7. F. M. Dong, Y. P. Liu, All wheels with two missing consecutive spokes are chromatically unique, Disc. Math., 184 (1998), 7185.
 8. M. R. Garey, D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP Completeness, Freeman, New York, 1979.
 9. F. Harary, R. A. Melter, On the metric dimension of a graph, Ars Combin., 2 (1976), 191195.
 10. M. Imran, A. Q. Baig, M. K. Shafiq, et al. On metric dimension of generlized Petersen graphs P(n, 3), Ars Combin., 117 (2014), 113130.
 11. M. Imran, A. Q. Baig, S. A. Bokhary, et al. On the metric dimension of circulant graphs, Appl. Math. Lett., 25 (2012), 320325.
 12. M. Imran, S. A. Bokhary, A. Q. Baig, On families of convex polytopes with constant metric dimension, Comput. Math. Appl., 60 (2010), 26292638.
 13. M. Imran, A. Ahmad, S. A. Bokhary, et al. On classes of regular graphs with constant metric dimension, Acta Math. Scientia, 33 (2013), 187206.
 14. M. Imran, H. M. A. Siddiqui, Computing the metric dimension of convex polytopes generated by wheel related graphs, Acta Math. Hungar., 149 (2016), 1030.
 15. I. Javaid, M. T. Rahim, K. Ali, Families of regular graphs with constant metric dimension, Utilitas Math., 75 (2008), 2133.
 16. S. Khuller, B. Raghavachari, A. Rosenfeld, Landmarks in graphs, Disc. Appl. Math., 70 (1996), 217229.
 17. S. Khuller, B. Raghavachari, A. Rosenfeld, Localization in graphs, Technical Report CSTR3326, University of Maryland at College Park, 1994.
 18. R. A. Melter, I. Tomescu, Metric bases in digital geometry, Comput. Vision Graphics, Image Processing, 25 (1984), 113121.
 19. O. R. Oellermann, J. PetersFransen, Metric dimension of Cartesian products of graphs, Utilitas Math., 69 (2006), 3341.
 20. M. Salman, I. Javaid, M. A. Chaudhry, Resolvability in circulant graphs, Acta Math. Sin. Engl. Ser., 28 (2012), 18511864.
 21. A. Sebö, E. Tannier, On metric generators of graphs, Math. Oper. Res., 29(2004),383393.
 22. H. M. A. Siddiqui, M. Imran, Computing the metric dimension of wheel related graphs, Appl. Math. Comput., 242 (2014), 624632.
 23. P. J. Slater, Leaves of trees, Congress. Numer., 14 (1975), 549559.
 24. P. J. Slater, Dominating and reference sets in graphs, J. Math. Phys. Sci., 22 (1988), 445455.
 25. I. Tomescu, M. Imran, On metric and partition dimensions of some infinite regular graphs, Bull. Math. Soc. Sci. Math. Roumanie, 52 (2009), 461472.
 26. I. Tomescu, I. Javaid, On the metric dimension of the Jahangir graph, Bull. Math. Soc. Sci. Math. Roumanie, 50 (2007), 371376.
 27. U. Ali, S. A. Bokhary, K. Wahid, et al. On resolvability of a graph associated to a finite vector space, Journal of Algebra and Its Applications, 18 (2018), 1950028.
Reader Comments
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)
Associated material
Metrics
Other articles by authors
Related pages
Tools
your name: * your email: *