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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
Zbl 0349.05118