On the spectral radius and energy of signless Laplacian matrix of digraphs

Hilal A. Ganie, Yilun Shang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
3 Downloads (Pure)


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)=Deg(D)+A(D), where A(D) is the adjacency matrix and Deg(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.

Original languageEnglish
Article numbere09186
Number of pages6
Issue number3
Early online date29 Mar 2022
Publication statusPublished - Mar 2022


Dive into the research topics of 'On the spectral radius and energy of signless Laplacian matrix of digraphs'. Together they form a unique fingerprint.

Cite this