On the general sum-connectivity index of connected unicyclic graphs with k pendant vertices

摘要

In this paper, we show that in the class of connected unicyclic graphs G of order n >= 3 having 0 <= k <= n - 3 pendant vertices, the unique graph G having minimum general sum-connectivity index chi(alpha)(G) consists of Cn-k and k pendant vertices adjacent to a unique vertex of Cn-k, if -1 <= alpha < 0. This property does not hold for zeroth-order general Randic index R-0(alpha) (G). (C) 2014 Elsevier B.V. All rights reserved.