关于Sumner-Blitch猜想的一个注记

设G是一个图。G的最小度，连通度，控制数，独立控制数和独立数分别用δ，k，γ，i和α表示，图G是3－γ-临界的，如果γ=3，而且G增加任一条边所得的图的控制数为2.Sumner和Blitch猜想：任意连通的3－γ临界图满足i=3，本文证明了如果G是使α＝k 1≤δ的连通3－γ-临界图，那么Sumner-Blitch猜想成立。

A Note on Sumner-Blitch's Conjecture

Let δ, κ, γ, i and α be the minimum degree, the connectivity, the domination number,the independent domination number and the independence number of a graph G, respectively. Thegraph G is 3-y-critical if γ = 3 and the addition of any edge decreases γ by 1. It was conjectured thatany connected 3-γ-critical graph satisfies i = 3. We show here that if G is a connected 3-γ-criticalgraph with a=κ+1 ≤δ, theni=3.