中文摘要：

设G为一简单连通图,则G的零阶广义Randic指数定义为Rα0（G）=∑ν∈V（G）dα（ν）,其中d（v）为顶点ν的度数,α为非0和1的实数.图G称之为仙人掌图,如果G的每一块要么是一条边,要么是一个圈.本文研究有r个悬挂点仙人掌图的零阶广义Randic指数的界.L（n,r）、G（n,r）、H（n,r）、M（n,r）、N（n,r）分别表示一类图.当α〈0时,Rα0G）取得极大值当且仅当G∈M（n,r）,Rα0取得极小值当且仅当G∈N（n,r）;当0〈α〈1时,Rα0取得极大值当且仅当G∈N（n,r）,Rα0取得极小值当且仅当G∈M（n,r）;当α〉1时,Rα0取得极大值当且仅当G∈G（n,r）,Rα0取得极小值当且仅当G∈H（n,r）.

英文摘要：

The zero-order general Randic index of a simple connected graph G is defined as R0α（G）=∑ν∈V（G）dα（ν）,where d（ν） denotes the degree of ν,α is a given real number other than 0 and 1.A graph G is called a cactus if each block of G is either an edge or a cycle.In this paper,we present the sharp bounds of the zero-order general Randic index of cacti with r pendents.L（n,r）,G（n,r）,H（n,r）,M（n,r）andN（n,r） denote some class of cacti respectvely.When α0,the maximal graph is in M（n,r） and the minimal graph is in N（n,r）;when 0α1,the maximal graph is in N（n,r）and the minimal graph is in M（n,r）;when α1,the maximal graph is in G（n,r）and the minimal graph is in H（n,r）.