Colin de Verdière parameters of chordal graphs

Abstract

The Colin de Verdi`ere parameters, μ and ν, are defined to be the maximum nullity of certain real symmetric matrices associated with a given graph. In this work, both of these parametersare calculated for all chordal graphs. For ν the calculation is based solely on maximal cliques, while for μ the calculation depends on split subgraphs. For the case of μ our work extends some recent work on computing μ for split graphs.