关于图的幂传播时间

摘要：

本文给出了图及其补图的功率传播时间之和的Nordhaus-Gaddum上界和下界，并考虑了边剖分和边收缩对图的功率传播时间的影响.我们还研究了一个泛化的功率传播时间，称为$k-$功率传播时间，通过表征$n$顶点的$k-$功率传播时间是$n-1$或$n-2$（对于$k\geq 1$）和$n-3$（对于$k\geq 2$）的所有单图。确定了$n$顶点上所有功率传播时间（$k=1$）为$n-3$的树，并给出了$k-$功率传播时间等于1（对于$k\geq 1$）的图的部分刻画.

英文摘要：

In this paper, we give Nordhaus-Gaddum upper and lower bounds on the sum of the power propagation time of a graph and its complement, and we consider the effects of edge subdivisions and edge contractions on the power propagation time of a graph. We also study a generalization of power propagation time, known as $k-$power propagation time, by characterizing all simple graphs on $n$ vertices whose $k-$power propagation time is $n-1$ or $n-2$ (for $k\geq 1$) and $n-3$ (for $k\geq 2$). We determine all trees on $n$ vertices whose power propagation time ($k=1$) is $n-3$, and give partial characterizations of graphs whose $k-$power propagation time is equal to 1 (for $k\geq 1$).

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