The mixed metric dimension mdim(G) of a graph G is the cardinality of a smallest set of vertices that (metrically) resolves each pair of elements from V (G)∪E(G).We saythat G is a max-mdim graph if mdim(G) = n(G). It is proved that a max-mdim graph G with n(G) ≥ 7 contains a vertex of degree at least 5. Using the strong product of graphs and amalgamations, large families of max-mdim graphs are constructed. The mixed metric dimension of graphs with at least one universal vertex is determined. The mixed metric dimension of graphs G with cut vertices is bounded from the above and the mixed metric dimension of block graphs computed.

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