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The problem of determining resolving sets in graph theory has a long history,as it has many applications in chemistry, robot navigation, combinatorialoptimization and utilization of the idea in pattern recognition and processingof images that also provide motivation for founding the theory. Especially, itis well known that these problems are NP hard. In the present work, first wedefine the structure of the crystal cubic carbon $CCC(n)$ by a new method, andwe will find the minimum number of doubly resolving sets and strong resolvingsets for the crystal cubic carbon $CCC(n)$. Also, we construct a new class ofgraphs of order $n+ \Sigma_{p=2}^{k}n^2(n-1)^{p-2}$, is denoted by $LCG(n, k)$and recall that the layer cycle graph with parameters $n$ and $k$. Moreover, wewill compute the minimum number of some resolving sets for the layer cyclegraph $LCG(n, k)$.

The minimum number of some resolving sets for the Crystal Cubic Carbon CCC(n) and the Layer Cycle Graph LCG(n, k)