文章讨论了树的独立数与其补图的独立数的关系,得到了:(1)若T为一棵,2(≥2)阶树,则 △+2≤α(T)+α(T^c)≤{n-(n-1/△)+2 r(n-1/△)=0 n-(n-1/△)+1 r(n-1/△)≠0 (2)设T为一棵n(≥4)阶树,α(T)=n-2当且仅当T具有给定的两种结构.
In this paper we discuss the relation between the independent numbers of tree and its complement,and obtain that: (1)Let T be a nontrivial tree with order n(≥2). Then △+2≤α(T)+α(T^c)≤{n-(n-1/△)+2 r(n-1/△)=0 n-(n-1/△)+1 r(n-1/△)≠0 (2)Let T be a nontrivial tree with order n(≥4). Then a(T) =n-2 if and only if T have the two structures.