id: 06034488
dt: j
an: 06034488
au: Sinkovic, John; Kempton, Mark
ti: Minimum rank of outerplanar graphs.
so: Linear Algebra Appl. 436, No. 9, 3701-3720 (2012).
py: 2012
pu: Elsevier Science Inc. (North-Holland), New York, NY
la: EN
cc: 
ut: minimum rank; positive semidefinite minimum rank; graph; outerplanar;
    inertia set; symmetric; cover; universally optimal matrix
ci: 
li: doi:10.1016/j.laa.2012.01.008
ab: Summary: The problem of finding the minimum rank over all symmetric
    matrices corresponding to a given graph has grown in interest recently.
    It is well known that the minimum rank of any graph is bounded above by
    the clique cover number, the minimum number of cliques needed to cover
    all edges of the graph. We generalize the idea of the clique cover
    number by defining the rank sum of a cover to be the sum of the minimum
    ranks of the graphs in the cover. Using this idea we obtain a
    combinatorial solution to the minimum rank problem for an outerplanar
    graph. As a consequence the minimum rank of an outerplanar graph is
    field independent and all outerplanar graphs have a universally optimal
    matrix. We also consider implications of the main result to the inverse
    inertia problem.
rv: