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Metric dimension of wheels. (English) Zbl 1032.05044
Summary: In [Ars Comb. 2, 191-195 (1976; Zbl 0349.05118)], F. Harary and R. A. Melter mentioned that the metric dimension of wheel \(W_{1,n}\) is \(2\). However, this result will not hold for large values of \(n\). In the same paper, they noted that \(\beta(K_p)= p-1\) and hence it follows that \(\beta(W_{1,3})= \beta(K_4)= 3\neq 2\). Making this observation, we compute the actual metric dimension of wheels. We also disprove \(\beta(G_1+ G_2)= \beta(G_1)+ \beta(G_2)\) mentioned in their paper.

MSC:
05C12 Distance in graphs
05C35 Extremal problems in graph theory
Citations:
Zbl 0349.05118
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