Sharp bounds for the signless Laplacian spectral radius of digraphs

Merging the A- and Q-spectral theories for digraphs

“…Let D(G) be the diagonal matrix with outdegrees of vertices of a digraph G. In this paper we study hybrids of A(G) and D(G) similar to the signless Laplacian matrix Q(G) = D(G) + A(G), which has been extensively studied since then. For detailed coverage of this research see [9,10,11,17,23,24], and their references. The study of Q(G) has shown that it is a remarkable matrix, and unique in many respects.…”

Spectral properties of digraphs with a fixed dichromatic number

“…At the end of this section the reader will find a small example to illustrate these matrices. Among the mostly studied matrices, we focus on the adjacency matrix A(G) [11,14,59,106,112,119], the Laplacian matrix L(G) [2,5,107,110,136], the signless Laplacian matrix Q(G) [10,55,65,72,131], the distance matrix D(G) [30,44,79,82,129], and the A α -matrix A α (G) [4,40,89,130,133]. We refer the interested reader to the following sources for details on other digraph matrices [53,71,74,128,132].…”

“…In 2022, Shan et al [115] characterized the extremal digraphs with the maximal or minimal α-spectral radius among some digraph classes, such as rose digraphs, generalized theta digraphs, and tri-ring digraphs with given size m. In 2023, Ganie and Carmona [41] established an increasing sequence of lower bounds for the spectral radius of digraphs. For more results on digraphs see [4,10,39,40,42,55,59,64,65,71,82,89,128,[130][131][132]. In this thesis, we mainly study the spectral radii of the A α -matrix and the eccentricity matrix of digraphs.…”