Trees of extremal connectivity index

The connectivity index w(G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where is a real number ( = 0), and d(u) denotes the degree of the vertex u. Let T be a tree with n vertices and k pendant vertices. In this paper, we give sharp lower and upper bounds for w1(T). Also, for -1 < 0, we give a sharp lower bound and a upper bound for w(T).

• Type: Journal
• Year: 2006
• Where: DAM
• Authors: Huiqing Liu, Mei Lu, Feng Tian
• Keywords: Connectivity Index, DAM 2006, Edges Uv, Real Number