On the extremal connectivity index of trees with k pendant vertices - Geng, Xianya; Li, Shuchao (Utilitas Mathematica, 2012)
The connectivity index w α(G) of a graph G is the sum of the weights (d(u)d(v)) αof all edges uv of G, where α is a nonzero real number and d(u) denotes the degree of the vertex u. Let J n,k be the set of trees on n vertices with k pendant vertices. Liu, Lu and Tian [Discrete Appl. Math., 154:106-119,2006] determined the sharp upper and lower bounds of w 1(T) for T ε n, k- In this paper, as a continuous of it, we characterize all the trees in .J n, k with the second largest and second smallest w 1-values.