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2013

On eigenvalues of Seidel matrices and Haemers' conjecture

Ghorbani, Ebrahim

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For a graph $G$, let $S(G)$ be the Seidel matrix of $G$ and $\te_1(G),...,\te_n(G)$ be the eigenvalues of $S(G)$.

The Seidel energy of $G$ is defined as $|\te_1(G)|+...+|\te_n(G)|$.
Willem Haemers conjectured that the Seidel energy of any graph with $n$ vertices is at least $2n-2$, the Seidel energy of the complete graph with $n$ vertices.
Motivated by this conjecture, we prove that for any $\al$ with $0<\al<2$, $|\te_1(G)|^\al+...+|\te_n(G)|^\al\g (n-1)^\al+n-1$ if and only if $|{\rm det} S(G)|\g n-1$.

On eigenvalues of Seidel matrices and Haemers' conjecture · Around

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O.L. Mangasarian and S. Fromovitz, The Fritz John necessary optimality conditions in the presence of equality and inequality constraints, J. Math. Anal. Appl
1967
Earlier work this paper cites.
J. Nocedal and S.J. Wright, Numerical Optimization
Original
2006
Earlier work this paper cites.

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S. Akbari, E. Ghorbani, J.H. Koolen, and M.R. Oboudi, On sum of powers of the Laplacian and signless Laplacian eigenvalues of graphs, Electron. J. Combin
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Then

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