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 min...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.展开更多
基金Supported by NSFC(No.12011530064)Natural Science Foundation of Shanghai(No.22ZR1416300)。
文摘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.
