Abstract：Let G be a connected graph. The connectivity κ(G) of a connected graph G is the least positive integer k such that there is F⊂V,|F|=k, and G-F is disconnected or is a trivial graph. If every minimum vertex cut isolates a vertex of G, a graph G is super connected or super-κ. Define the inverse degree of a graph G with no isolated vertices as R(G)=1/(d(v)). In this paper, we show that let G be a connected graph with order n and minimum degree δ, if R(G)<1+2/(δ+1)+(n-2δ-1)/((n-1)(n-3)), then G is super-κ.
作者简介: 郭利涛(1982-),ORCID:http://orcid.org/0000-0003-1410-8509,male,doctor,associate professor,the field of interest is graph theory,E-mail:ltguo2012@126.com.
引用本文:
郭利涛. 超连通图的充分条件[J]. 浙江大学学报（理学版）, 2018, 45(4): 391-393.
GUO Litao. Sufficient conditions for graphs to be super connected. Journal of ZheJIang University(Science Edition), 2018, 45(4): 391-393.
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2018, Vol. 45 
1/（d（v））.得到：设n阶连通图G，最小度为δ，若R（G）<1+2/（δ+1）+（n-2δ-1）/（（n-1）（n-3）），则G是超-κ的.
1/(d(v)). In this paper, we show that let G be a connected graph with order n and minimum degree δ, if R(G)<1+2/(δ+1)+(n-2δ-1)/((n-1)(n-3)), then G is super-κ.