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arXiv · 1605.05692

Expected values of parameters associated with the minimum rank of a graph

Tracy Hall·Leslie Hogben·Ryan R. Martin·Bryan Shader
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Abstract

We investigate the expected value of various graph parameters associated with the minimum rank of a graph, including minimum rank/maximum nullity and related Colin de Verdi\`ere-type parameters. Let $G(v,p)$ denote the usual Erd\H{o}s-R\'enyi random graph on $v$ vertices with edge probability $p$. We obtain bounds for the expected value of the random variables ${\rm mr}(G(v,p))$, ${\rm M}(G(v,p))$, $\nu(G(v,p))$ and $\xi(G(v,p))$, which yield bounds on the average values of these parameters over all labeled graphs of order $v$.

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Tracy Hall, Leslie Hogben, Ryan R. Martin, Bryan Shader. 2016-05-18. Expected values of parameters associated with the minimum rank of a graph. https://doi.org/10.1016/j.laa.2010.01.036

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