Degree Powers of Minimally k-(edge)-connected Graphs  

极小k-(边)-连通图的度幂

作　　者：MENG Canjun ZHANG Liwen 孟灿君;张力文(华东理工大学数学学院,上海200237)

机构地区：[1]School of Mathematics,East China University of Science and Technology,Shanghai,200237,P.R.China

出　　处：《数学进展》2024年第6期1173-1180,共8页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.12011530064);Natural Science Foundation of Shanghai(No.22ZR1416300)。

摘　　要：Let G be a graph on n vertices whose degree sequence is d_(1)≥…≥d_(n).For a positive integer p,the degree power of G is defined by e_p(G)=∑_(i=1)^(n) d_(i)^(p).In this paper,by majorization,we prove that for a minimally k-connected graph G of order n≥4k,it always holds e_(2)(G)≤kn(n-k)and the extremal graph is K_(k,n-k).Furthermore,we respectively determine the maximum degree powers among all minimally 2(3)-connected graphs and minimally 2-edgeconnected graphs,whose extremal graphs are also characterized.设图G的顶点数为n,度序列为d_(1)≥…≥d_(n).对正整数p,图G的度幂定义为e_(p)(G)=∑_(i=1)^(n)d_(i)^(p).本文利用优超证明了顶点数n≥4k的极小k-连通图满足e_(2)(G)≤kn(n-k),且极图为K_(k,n-k).进一步,本文分别确定了极小2(3)-连通图和极小2-边-连通图的最大度幂,并刻画了相应的极图.

关 键 词：degree power majorization minimally k-connected graph 

分 类 号：O157.5[理学—数学]