On the null space of a Colin de Verdière matrix

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On the null space of a Colin de Verdière matrix

Let G = (V, E) be a 3-connected planar graph, with V = {1, . . . , n}. Let M = (mi,j) be a symmetric n×n matrix with exactly one negative eigenvalue (of multiplicity 1), such that for i, j with i 6= j, if i and j are adjacent then mi,j < 0 and if i and j are nonadjacent then mi,j = 0, and such that M has rank n− 3. Then the null space ker M of M gives an embedding of G in S as follows: Let a, b...

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ژورنال

عنوان ژورنال: Annales de l’institut Fourier

سال: 1999

ISSN: 0373-0956

DOI: 10.5802/aif.1703