The degree-associated reconstruction number of an unicentroidal tree

As we know, by deleting one vertex of a graph G, we have a subgraph of G called a card of G. Also, investigation of that each graph with at least three vertices is determined by its multiset of cards, is called the reconstruction conjecture and the minimum number of dacards that determine G is denoted the degree-associated reconstruction number drn(G). Barrus and West conjectured that drn(G) ≤ 2 for all but finitely many trees. A tree is unicentroidal or bicentroidal when it has one or two centroids, respectively. An unicentroidal tree T with centroid v is symmetrical if for two neighbours of u and u′ of v, there exists an automorphism on T mapping u to u′. In [10], Shadravan and Borzooei proved that the conjecture is true for any non-symmetrical unicentroidal tree. In this paper, we proved that for any symmetrical unicentroidal tree T, drn(T) ≤ 2. So, we concluded that the conjecture is true for any unicentroidal tree.