Computing the upper bounds for the metric dimension of cellulose network

Let G = (V, E) be a connected graph and d(x, y) be the distance between the vertices x and y in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by dim(G). In this paper we study three dimensional chemical structure of cellulose network and then we converted it into planar chemical structure, consequently we obtained cellulose network graphs denoted by CL^kn. We prove that dim(CL^kn) ≤ 4 in certain cases.