有r个悬挂点仙人掌图的零阶广义Randic指数的界  

On Bounds of Zero-order General Randic Index of Cacti with r Pendents

作　　者：吕宁宁[1] 马艳丽[1] 

机构地区：[1]安徽新华学院公共课教学部,安徽合肥230088

出　　处：《河北北方学院学报（自然科学版）》2011年第5期1-5,12,共6页Journal of Hebei North University:Natural Science Edition

基　　金：国家自然科学基金项目(10901001);安徽新华学院资助科研项目(2011zr006);安徽新华学院资助科研项目(2011zr007)

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).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）.

关 键 词：仙人掌图 零阶广义RANDIC指数 界 

分 类 号：O157.5[理学—数学]