论文标题
多个边分段的关键图
Critical graphs upon multiple edge subdivision
论文作者
论文摘要
如果每个顶点的$ v-d $的每个顶点在$ d; $ d; $ d; let $ d; $ let $γ（g）$中至少有一个邻居是$g。 $γ（g）$具有基数$ q。$在本文中，我们认为主要是$γ$ - $ q $ - 关键树，并提供$ gamma $ - $ q $ - 限制图的一般属性。特别是，我们表明，如果$ t $是$γ$ - $ q $ - 重要的树，则$ 1 \ leq q \ leq n（t）-1 $，我们在$ q = n（t）-1时表征极端树。与$ {\ rm sd}（t）= 2 $和$γ$ -2 $ -X $ -3-CRICATION TROED $ {\ rm SD}（t）= 3
A subset $D$ of $V$ is \emph{dominating} in $G$ if every vertex of $V-D$ has at least one neighbour in $D;$ let $γ(G)$ be the minimum cardinality among all dominating sets in $G.$ A graph $G$ is $γ$-$q$-{\it critical} if the smallest subset of edges whose subdivision necessarily increases $γ(G)$ has cardinality $q.$ In this paper we consider mainly $γ$-$q$-critical trees and give some general properties of $gamma$-$q$-critical graphs. In particular, we show that if $T$ is a $γ$-$q$-critical tree, then $1 \leq q \leq n(T)-1$ and we characterize extremal trees when $q=n(T)-1.$ Since a subdivision number {of a tree $T$} ${\rm sd}(T)$ is always $1,2$ or $3,$ we also characterize $γ$-2-critical trees $T$ with ${\rm sd}(T)=2$ and $γ$-3-critical trees $T$ with ${\rm sd}(T)=3.$
