Max-plus objects to study the complexity of graphs

Details Max-plus objects to study the complexity of graphs Max-plus objects to study the complexity of graphs

2011-11-05

arxiv.org/abs/1111.1352v2

Mathematics

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16 pages, 7 figures. 2 figures were not displayed properly in the first version

Scientific paper

Given an undirected graph $G$, we define a new object $H_G$, called the mp-chart of $G$, in the max-plus algebra. We use it, together with the max-plus permanent, to describe the complexity of graphs. We show how to compute the mean and the variance of $H_G$ in terms of the adjacency matrix of $G$ and we give a central limit theorem for $H_G$. Finally, we show that the mp-chart is easily tractable also for the complement graph.

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