The Main Eigenvalues of the Seidel Matrix
Mathematica Moravica, Tome 12 (2008) no. 1.

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Let $G$ be a simple graph with vertex set $V(G)$ and $(0,1)$-adjacency matrix $A$. As usual, $A^{\ast}(G) = J-I-2A$ denotes the Seidel matrix of the graph $G$. The eigenvalue $\lambda$ of $A$ is said to be a main eigenvalue of $G$ if the eigenspace $\varepsilon(\lambda)$ is not orthogonal to the all-1 vector $\mathbf{e}$. In this paper, relations between the main eigenvalues and associated eigenvectors of adjacency matrix and Seidel matrix of a graph are investigated.
Mots-clés : Graph spectra, Main eigenvalues, Seidel matrix 
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Houqing Zhou. The Main Eigenvalues of the Seidel Matrix. Mathematica Moravica, Tome 12 (2008) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2008_12_1_a7/