Sum-connectivity indices of trees and unicyclic graphs of fixed maximum   degree
  We obtain the maximum sum-connectivity indices of graphs in the set of trees and in the set of unicyclic graphs respectively with given number of vertices and maximum degree, and determine the corresponding extremal graphs. Additionally, we deduce the n-vertex unicyclic graphs with the first two maximum sum-connectivity indices for $n\ge 4$. 
Zhibin Du, Bo Zhou, Nenad Trinajstic
math.CO