Local multiset dimension of corona product on tree graphs

One of the topics of distance in graphs is resolving set problem. This topic has many applications in science and technology namely navigation robots, chemistry structure, and computer sciences. Suppose the set W = {s₁, s₂, ⋯, s_k} ⊂ V (G), the vertex representations of x ∈ V (G) is r_m (x|W) = {d(x, s₁), d(x, s₂),⋯, d (x,s_k)}, where d (x,s_i) is the length of the shortest path of the vertex x and the vertex in W together with their multiplicity. The set W is called a local m-resolving set of graphs G if r_m(v|W) ≠ r_m (u|W) for uv ∈ E(G). The local m-resolving set having minimum cardinality is called the local multiset basis and its cardinality is called the local multiset dimension of G, denoted by md_l (G). In our paper, we determine the establish bounds of local multiset dimension of graph resulting corona product of tree graphs.