Max-Plus Objects to Study the Complexity of Graphs

Cristiano Bocci (), Luca Chiantini () and Fabio Rapallo ()
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Cristiano Bocci: Università di Siena
Luca Chiantini: Università di Siena
Fabio Rapallo: Università del Piemonte Orientale

Methodology and Computing in Applied Probability, 2014, vol. 16, issue 3, 507-525

Abstract: Abstract 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.

Keywords: Matchings; Combinatorial central limit theorem; Random permutations; Complement graph; 05C30; 60F05 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s11009-012-9311-x

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