Determinants of Seidel matrices and a conjecture of Ghorbani

2019/04/09 by Rizzolo, Douglas
#05C50 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1904.04870

Abstract

Let G_n be a simple graph on V_n=\v₁,…, v_n\. The Seidel matrix S(G_n) of G_n is the n× n matrix whose (ij)'th entry, for i≠ j is -1 if v_i∼ v_j and 1 otherwise, and whose diagonal entries are 0. We show that the proportion of simple graphs G_n such that det(S(G_n))≥ n-1 tends to one as n tends to infinity.

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