TY - JOUR

T1 - On the spectral radius and energy of signless Laplacian matrix of digraphs

AU - Ganie, Hilal A.

AU - Shang, Yilun

PY - 2022/3

Y1 - 2022/3

N2 - 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.

AB - 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.

KW - Digraphs

KW - Energy

KW - Generalized adjacency spectral radius

KW - Signless Laplacian spectral radius

KW - Strongly connected digraphs

UR - http://www.scopus.com/inward/record.url?scp=85127122874&partnerID=8YFLogxK

U2 - 10.1016/j.heliyon.2022.e09186

DO - 10.1016/j.heliyon.2022.e09186

M3 - Article

AN - SCOPUS:85127122874

VL - 8

JO - Heliyon

JF - Heliyon

SN - 2405-8440

IS - 3

M1 - e09186

ER -