Expected values of parameters associated with the minimum rank of a graph
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2010-07-01
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Hogben, Leslie
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Mathematics
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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 Verdière-type parameters. Let G(v,p) denote the usual Erdős-Rényi random graph on v vertices with edge probability p. We obtain bounds for the expected value of the random variables mr(G(v,p)), M(G(v,p)), ν(G(v,p)) and ξ(G(v,p)), which yield bounds on the average values of these parameters over all labeled graphs of order v.
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This is a manuscript of an article from Linear Algebra and its Applications 433 (2010): 401, doi:10.1016/j.laa.2010.01.036. Posted with permission.
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Fri Jan 01 00:00:00 UTC 2010