Geodesic
On Skew Laplacian Spectra and Skew Laplacian Energy of Digraphs
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 1, p. 87

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Let $\mathscr{D}$ be a simple digraph with $n$ vertices, $m$ arcs having skew Laplacian eigenvalues $\nu_1, \nu_2, …, \nu_{n-1},\nu_n=0$. The skew Laplacian energy $SLE(\mathscr{D})$ of a digraph $\mathscr{D}$ is defined as $SLE(\mathscr{D})=\sum_{i=1}^{n}|\nu_i|$. We obtain upper and lower bounds for $SLE(\mathscr{D})$, which improves some previously known bounds. We also show that every even positive integer is indeed the skew Laplacian energy of some digraph.
Classification : 05C50, 05C30
Keywords: Digraphs, skew Laplacian matrix, skew Laplacian spectrum, skew Laplacian energy 
Hilal Ganie; Bilal Chat; S. Pirzada. On Skew Laplacian Spectra and Skew Laplacian Energy of Digraphs. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 1, p. 87 . http://geodesic.mathdoc.fr/item/KJM_2019_43_1_a7/
@article{KJM_2019_43_1_a7,
     author = {Hilal Ganie and Bilal Chat and S. Pirzada},
     title = {On {Skew} {Laplacian} {Spectra} and {Skew} {Laplacian} {Energy} of {Digraphs}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {87 },
     year = {2019},
     volume = {43},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2019_43_1_a7/}
}
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