Geodesic
On the minimum vector rank of multigraphs
The electronic journal of linear algebra, Tome 20 (2010), pp. 661-672.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The minimum vector rank (mvr) of a graph over a field F is the smallest d for which a faithful vector representation of G exists in F d . For simple graphs, minimum semidefinite rank (msr) and minimum vector rank differ by exactly the number of isolated vertices. We explore the relationship between msr and mvr for multigraphs and show that a result linking the msr of chordal graphs to clique cover number also holds for the mvr of multigraphs. We study the difference between msr and mvr in the removal of duplicate vertices in multigraphs, and relate mvr to certain coloring problems.
Classification : 15A18, 05C50, 15A57
Keywords: minimum semidefinite rank, minimum vector rank, duplicate vertices, chordal graph 
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Mitchell, Lon H.; Narayan, Sivaram K.; Rogers, Ian. On the minimum vector rank of multigraphs. The electronic journal of linear algebra, Tome 20 (2010), pp. 661-672. http://geodesic.mathdoc.fr/item/ELA_2010__20__a7/