On the signless Laplacian energy of a digraph

Hilal A. Ganie ()
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Hilal A. Ganie: JK Govt. Kashmir

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 2, 555-570

Abstract: Abstract Let D be a digraph of order n and with a arcs. The eigenvalues of the signless Laplacian matrix Q(D), denoted by $$q_1(D),q_2(D),\dots ,q_n(D)$$ q 1 ( D ) , q 2 ( D ) , ⋯ , q n ( D ) , are the signless Laplacian eigenvalues of D. The signless Laplacian energy of D is defined as $$QE(D)=\sum \limits _{i=1}^{n}\Big |q_i(D)-\frac{a}{n}\Big |$$ Q E ( D ) = ∑ i = 1 n | q i ( D ) - a n | . The main contribution of this paper is a series of bounds for the signless Laplacian energy QE(D) and the characterization of the extremal digraphs for these bounds. We study the spectral radius and the signless Laplacian energy of signless Laplacian normal digraphs and characterize the extremal digraphs. Our bounds improve some known bounds in [12] and [22]. Moreover, our results generalize some important results obtained for graphs to digraphs.

Keywords: Digraphs; Strongly connected digraphs; Normal digraphs; Signless Laplacian spectral radius; Signless Laplacian energy; Primary: 05C50; 05C12; Secondary: 15A18 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00502-2

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