Let h be a nonnegative integer. The h-restricted edge connectivity λ h(G) of a simple connected graph G is defined as the minimum cardinality over the sets of edges of G, if any, whose removal disconnects G and every...Let h be a nonnegative integer. The h-restricted edge connectivity λ h(G) of a simple connected graph G is defined as the minimum cardinality over the sets of edges of G, if any, whose removal disconnects G and every component of the resulting graph has more than h vertices. This paper gave a necessary and sufficient condition and also three useful sufficient conditions to guarantee the existence of λ h(G). Moreover, it explicitly characterized the graphs whose 2-restricted edge connectivities do not exist.展开更多
Ghouila—Houri 得到强连通有向图 D 是有向 H 图的充分条件.强连通有向图 D 中,若对任一点 V.d((?))≥p,则 D 是有向 H 图。任一有向图都可以看作某个相应马尔可夫链的转移概率图。我们应用马尔可夫链理论得到:强连通有向图 D 中,如果 ...Ghouila—Houri 得到强连通有向图 D 是有向 H 图的充分条件.强连通有向图 D 中,若对任一点 V.d((?))≥p,则 D 是有向 H 图。任一有向图都可以看作某个相应马尔可夫链的转移概率图。我们应用马尔可夫链理论得到:强连通有向图 D 中,如果 min{δ^+(D),δ^-(D)}≥p/d,则 D 是有向 H图。这里 d 是马尔可夫链周期,因此 d≥2。当 d=2时,即是 Ghouil—Houri 定理条件。展开更多
基金National Natural Science Foundation of China( No.199710 5 6)
文摘Let h be a nonnegative integer. The h-restricted edge connectivity λ h(G) of a simple connected graph G is defined as the minimum cardinality over the sets of edges of G, if any, whose removal disconnects G and every component of the resulting graph has more than h vertices. This paper gave a necessary and sufficient condition and also three useful sufficient conditions to guarantee the existence of λ h(G). Moreover, it explicitly characterized the graphs whose 2-restricted edge connectivities do not exist.
文摘Ghouila—Houri 得到强连通有向图 D 是有向 H 图的充分条件.强连通有向图 D 中,若对任一点 V.d((?))≥p,则 D 是有向 H 图。任一有向图都可以看作某个相应马尔可夫链的转移概率图。我们应用马尔可夫链理论得到:强连通有向图 D 中,如果 min{δ^+(D),δ^-(D)}≥p/d,则 D 是有向 H图。这里 d 是马尔可夫链周期,因此 d≥2。当 d=2时,即是 Ghouil—Houri 定理条件。
