The mixed metric dimension of flower snarks and wheels

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

On the Metric Dimension for Snowflake Graph

The concept of metric dimension is derived from the resolving set of a graph, that is measure the diameter among vertices in a graph. For its usefulness in diverse fields, it is interesting to find the metric dimension of various classes of graphs. In this paper, we introduce two new graphs, namely snowflake graph and generalized snowflake graph. After we construct these graphs, aided with a lemma about the lower bound of the metric dimension on a graph that has leaves, and manually recognized the pattern, we found that dim(Snow) = 24 and dim(Snow(n,a,b,c)) = n(a+c+1)