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22nd Cumberland Conference on Combinatorics, Graph Theory and Computing
May 21-23, 2009
Western Kentucky University
Bowling Green, KY, USA

Organizers
Bela Csaba, Chair; Mustafa Atici; Robert Crawford; Claus Ernst; Dominic Lanphier; Attila Por

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Expected value of the minimum rank of a graph
by
Ryan R. Martin
Dept. of Mathematics, Iowa State University
Coauthors: Tracy Hall, Leslie Hogben and Bryan Shader

We associate a symmetric real matrix, M, with a graph, G, if mij is nonzero whenever distinct vertices vi and vj are adjacent and is zero whenever distinct vertices vi and vj are nonadjacent. The diagonal is unrestricted. The minimum rank of G, denoted mr(G), is the minimum of the ranks of all matrices associated with G. We obtain bounds for mr(G(n, p)) for fixed p and n sufficiently large. We use concentration results for graph parameters, bounds on the number of zero patterns of polynomials with bounded degree and faithful orthogonal representations of graphs by vectors.

Date received: April 30, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayq-53.