线图连通度的界

The Bounds for the Connectivity of Line Graphs

首先给出了线图连通度K_L的一个上界:K_L≤δ+Δ-2;其次得出了在条件δ≥[n/2]+1下K_L的一个很好的下界:K_L≥2δ-2;由此得到当δ≥[n/2]+1时,若G为正则图,则K_L=2δ-2,若G为拟正则图,则K_L=2δ-2或2δ-1.

An upper bound and lower bounds for the connectivity of the line graph L(G) are determined. The upper bound is presented as KL≤δ+△-2 in general,and an advanced lowerbound is carried out in the form KL≥2δ-2 when δ≥[n/2] +1. Some other results are given,especially,if δ≥[n/2]+1,then kL = 2δ- 2 over the regular graph and kl = 2δ - 2 or 2δ-1 over the quasi-regular graph.