K(1,4)-自由的模k泛圈图(英文)

设G是2-连通的K1,4自由图.本文证明了当δ(G)≥k 1时,G是模k泛圈图.这一结果肯定了猜想2,继而也肯定了Thomassen猜想在2-连通图中的正确性.     

K_m∨的最小直径定向(英文)

For a graph G,let D denote an orientation of G having minimum diameter. Define f(G)=diamD.In this paper,we concentrate on exploring the minimum diameter of K_m∨(m≥1,n≥1).Some special cases are known:f(K_m∨)=∞,2,3, where m=1 and n≥1,m=2 or m≥4 and n=1,m=3 and n=1,respectively. So we only consider the case when m≥2 and n≥2.The following results are obtained. (1) f(K_m∨)=3,where m=2,3,n≥2 and m=n=4.(2) f(K_m∨)=2, where m≥5 and m is odd,2≤n≤■-m.(3) f(K_m∨)=2,where m≥4 and m≡0(mod4),2≤n≤■-(m/2 1).(4) f(K_m∨)=2,where m≥6 and m≡2(mod4),2≤n≤■-m/2.(5) f(K_m∨)=3,where m≥4,n>■.     

K1,4-自由的模κ泛圈图

设G是2-连通的K1，4自由图．本文证明了当δ(G)≥κ 1时，G是模κ泛圈图．这一结果肯定了猜想2，继而也肯定了Thomassen猜想在2-连通图中的正确性．     

关于谱确定乘积图的若干结果

In this paper, we prove that some Kronecker products of G and K2 are determined by their spectra where the graph G is also determined by its spectrum. And a problem for further researches is proposed.