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The mixed metric dimension of flower snarks and wheels. (English) Zbl 1475.05055

Summary: New graph invariant, which is called a mixed metric dimension, has been recently introduced. In this paper, exact results of the mixed metric dimension on two special classes of graphs are found: flower snarks \(J_n\) and wheels \(W_n\). It is proved that the mixed metric dimension for \(J_5\) is equal to 5, while for higher dimensions it is constant and equal to 4. For \(W_n\), the mixed metric dimension is not constant, but it is equal to \(n\) when \(n\ge 4\), while it is equal to 4, for \(n=3\).

MSC:

05C12 Distance in graphs
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