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On metric dimension of some rotationally symmetric graphs. (English) Zbl 1264.05041

Summary: A family \(\mathcal{G}\) of connected graphs is a family with constant metric dimension if \(\dim(G)\) is finite and does not depend upon the choice of \(G\) in \(\mathcal{G}\). In this paper, we show that the graph \(A^\ast_n\) and the graph \(A^p_n\) obtained from the antiprism graph have constant metric dimension.

MSC:

05C12 Distance in graphs
05C40 Connectivity
05C75 Structural characterization of families of graphs
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References:

[1] G. Chartrand, L. Eroh, M. A. Johnson, and O. R. Oellermann, “Resolvability in graphs and the metric dimension of a graph,” Discrete Applied Mathematics, vol. 105, no. 1-3, pp. 99-113, 2000. · Zbl 0958.05042
[2] J. Caceres, C. Hernando, M. Mora et al., “On the metric dimension of some families of graphs,” Electronic Notes in Discrete Mathematics, vol. 22, pp. 129-133, 2005. · Zbl 1182.05050
[3] I. Javaid, M. Salman, M. A. Chaudhry, and S. Shokat, “Fault-tolerance in resolvability,” Utilitas Mathematica, vol. 80, pp. 263-275, 2009. · Zbl 1197.05041
[4] I. Javaid, M. T. Rahim, and K. Ali, “Families of regular graphs with constant metric dimension,” Utilitas Mathematica, vol. 75, pp. 21-33, 2008. · Zbl 1178.05037
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