Geodesic
Some Properties of the Eigenvalues of the Net Laplacian Matrix of a Signed Graph
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 893-903

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Given a signed graph Ġ, let A_Ġ and D_Ġ^± denote its standard adjacency matrix and the diagonal matrix of vertex net-degrees, respectively. The net Laplacian matrix of Ġ is defined to be N_Ġ = D_Ġ^± - A_Ġ. In this study we give some properties of the eigenvalues of N_Ġ. In particular, we consider their behaviour under some edge perturbations, establish some relations between them and the eigenvalues of the standard Laplacian matrix and give some lower and upper bounds for the largest eigenvalue of N_Ġ.
Keywords: (net) Laplacian matrix, edge perturbations, largest eigenvalue, net-degree 
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Stanić, Zoran. Some Properties of the Eigenvalues of the Net Laplacian Matrix of a Signed Graph. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 893-903. http://geodesic.mathdoc.fr/item/DMGT_2022_42_3_a12/