On the connectivity index of trees

• DOI: 10.1007/s10910-007-9281-3
• Publication Date: 2007-09-20T17:47:30Z
• Authors: Yue Jiang; Mei Lu
• Keywords: 0101 mathematics; 01 natural sciences

The connectivity index χ1(G) of a graph G is the sum of the weights d(u)d(v) of all edges uv of G, where d(u) denotes the degree of the vertex u. Let T(n, r) be the set of trees on n vertices with diameter r. In this paper, we determine all trees in T(n, r) with the largest and the second largest connectivity index. Also, the trees in T(n, r) with the largest and the second largest connectivity index are characterized.