Survey of adjacency spectra results for signed graphs and open problems that generalize those studied for unsigned graphs.
Determinants of Seidel matrices and a conjecture of Ghorbani
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abstract
Let $G_n$ be a simple graph on $V_n=\{v_1,\dots, v_n\}$. The Seidel matrix $S(G_n)$ of $G_n$ is the $n\times n$ matrix whose $(ij)$'th entry, for $i\neq j$ is $-1$ if $v_i\sim v_j$ and $1$ otherwise, and whose diagonal entries are $0$. We show that the proportion of simple graphs $G_n$ such that $\det(S(G_n))\geq n-1$ tends to one as $n$ tends to infinity.
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math.CO 1years
2019 1verdicts
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Open problems in the spectral theory of signed graphs
Survey of adjacency spectra results for signed graphs and open problems that generalize those studied for unsigned graphs.