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- W1788346711 abstract "A signed graph is a pair ( G , Σ ) , where G = ( V , E ) is a graph (in which parallel edges are permitted, but loops are not) with V = { 1 , … , n } and Σ ⊆ E . The edges in Σ are called odd and the other edges even. By S ( G , Σ ) we denote the set of all real symmetric n × n matrices A = [ a i , j ] with a i , j < 0 if i and j are adjacent and all edges between i and j are even, a i , j > 0 if i and j are adjacent and all edges between i and j are odd, and a i , j = 0 if i ≠ j and i and j are non-adjacent. The parameter ν ( G , Σ ) of a signed graph ( G , Σ ) is the largest nullity of any positive semidefinite matrix A ∈ S ( G , Σ ) that has the Strong Arnold Property. By K 3 = we denote the signed graph obtained from ( K 3 , ∅ ) by adding to each even edge an odd edge in parallel. In this paper, we prove that a signed graph ( G , Σ ) has ν ( G , Σ ) ≤ 2 if and only if ( G , Σ ) has no minor isomorphic to ( K 4 , E ( K 4 ) ) or K 3 = ." @default.
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- W1788346711 date "2016-01-01" @default.
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- W1788346711 title "Signed graphs whose signed Colin de Verdière parameter is two" @default.
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- W1788346711 doi "https://doi.org/10.1016/j.jctb.2015.09.007" @default.
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