On the power propagation time of a graph

Chassidy Bozeman

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arXiv · 1608.01189

On the power propagation time of a graph

Chassidy Bozeman

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Abstract

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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Chassidy Bozeman. 2016-08-03. On the power propagation time of a graph. https://arxiv.org/abs/1608.01189

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