一种变形对树的代数连通度的影响

Effect of Algebraic Connectivity of a Disformed Logarithmetic

设T是一个树,uv是T的一条边,其中d(v)=2.考虑经过一种特殊的变形后树的代数连通度的变化为:收缩边uv,并以收缩后的点u(v)为端点增加一条新的悬挂边,这样得到的新树记为T′,则α(T)≤α(T′).

If T is a tree, and uv is an edge of T, where d（v） = 2. This paper investigates how the algebraic connectivity changes under the perturbation： by contracting the edge uv, and adding a pendent edge at the new vertex u（v）, and resulting in a new tree T＇, thenα（T）≤α（T＇）.