The Minimum Randic Index Of Tree With N Vertices And K Matches

Let G = (V , E)be a simple and conneted graph with the vertex set V (G ) and the edge set E (G ).The Randic index of the graph G is defined as following: where d (u ) is the degree of vertex u . The Randicindex of the graph is one of the most important topological indices in chemical graph theory. It has a lot of applications in chemistry, it has been widely investigated as well. Let T n ,k be the set of trees with n vertices and k matches. Let R (G ) be the Randic index of the graph G .In this paper, we use mathematical induction to prove and describe the character of the tree which has the minimum Randic index in the set T n ,k, meanwhile, the minimum Randic index is also given among T∈T n ,k: If T∈T n ,k, then . Besides we give the minimum Randic index which has the perfect match.