摘要
记G=(V,E)是简单图,δ表示图G的最小度,NC=min{|N(x)∪N(y)|:x,y∈V(G),xy(?)E(G)},NC_2=min{|N(x)∪N(y)|:x,y∈V(G),d(x,y)=2}。1989年Faudree等证明了:若3连通n阶图G,NC≥(2n+1)/3,则G是哈密尔顿连通图。据此进一步研究NC_2≥(2n+1)/3,而且研究到2连通图,得到下面结果:若2连通n阶图G,NC_2≥(2n+1)/3,则G是哈密尔顿连通图或G=φ。
Let G = (V, E) be a sample graph, NC = min {|N(x)∪N(y)|; x,y∈V(G),xy∈E(G)}, NC_2 =min{|N(x)∪N(y)|; x, y ∈V(G), d(x,y)=2}. In 1989, Faudree et al obtained that if 3-connected graph G of order nwith NC≥(2n+1)/3,then G be Hamiltonian-connected graph. If 2-connected graph G of order n with NC_2 ≥(2n+1)/3,then G be Hamiltonian-connected graph or G=ψ.
出处
《科学技术与工程》
2003年第4期315-317,共3页
Science Technology and Engineering
