On the spectral radius and energy of signless Laplacian matrix of digraphs. Issue 3 (March 2022)

• Record Type: Journal Article
• Authors: Ganie, Hilal A.; Shang, Yilun
• Is Part Of: Heliyon. Volume 8:Issue 3(2022)
• Publication Date: 2022-03
• Subjects: Digraphs -- Strongly connected digraphs -- Signless Laplacian spectral radius -- Generalized adjacency spectral radius -- Energy; Research -- Periodicals; Medical sciences -- Periodicals; Natural history -- Periodicals; Social sciences -- Periodicals; Earth sciences -- Periodicals; Physical sciences -- Periodicals; 507.2
• DOI: 10.1016/j.heliyon.2022.e09186
• Languages: English
• ISSNs: 2405-8440

Abstract

Abstract: Let D be a digraph of order n and with a arcs. The signless Laplacian matrix Q ( D ) of D is defined as Q ( D ) = D e g ( D ) + A ( D ), where A ( D ) is the adjacency matrix and D e g ( D ) is the diagonal matrix of vertex out-degrees of D . Among the eigenvalues of Q ( D ) the eigenvalue with largest modulus is the signless Laplacian spectral radius or the Q -spectral radius of D . The main contribution of this paper is a series of new lower bounds for the Q -spectral radius in terms of the number of vertices n, the number of arcs, the vertex out-degrees, the number of closed walks of length 2 of the digraph D . We characterize the extremal digraphs attaining these bounds. Further, as applications we obtain some bounds for the signless Laplacian energy of a digraph D and characterize the extremal digraphs for these bounds. Abstract : Digraphs; Strongly connected digraphs; Signless Laplacian spectral radius; Generalized adjacency spectral radius; Energy