Let λ (D) be the A α spectral radius of digraph D, and let G nr be the set of digraphs with
order n and dichromatic number r. In this paper, we characterize the digraph which has the …

Let G be a digraph and A (G) be the adjacency matrix of G. Let D (G) be the diagonal matrix
with outdegrees of vertices of G. For any real α∈[0, 1], define the matrix A α (G) as A α (G)= α …

Let D be a strongly connected digraph and A (D) be the adjacency matrix of D. Let diag (D)
be the diagonal matrix with outdegrees of the vertices of D and Q (D)= diag (D)+ A (D) be the …

Let q (G) and μ (G) denote the signless Laplacian and distance signless Laplacian spectral
radius of a digraph G, respectively. In this paper, we characterize the extremal digraph which …

Let D be a digraph with vertex set V (D) and A be the adjacency matrix of D. The largest
eigenvalue of A, denoted by ρ (D), is called the spectral radius of the digraph D. In this …

In the thesis, the coloring of digraphs is studied. The chromatic number of a digraph D is the
smallest integer k so that the vertices of D can be partitioned into at most k sets each of …

For any real number α∈[0, 1] and a graph G, Nikiforov [20] defined matrix A α (G) as A α
(G)= α D (G)+(1− α) A (G). The A α-spectral radius of G is the largest eigenvalue of A α (G). In …

We consider the extension to directed graphs of the concept of achromatic number in terms
of acyclic vertex colorings. The achromatic number have been intensely studied since it was …

Abstract Let D (G ⃗) denote the distance matrix of a strongly connected digraph G ⃗. The
eigenvalue of D (G ⃗) with the largest modulus is called the distance spectral radius of a …

In 1972, Cvetković proved that if G is an n-vertex simple graph with the chromatic number k,
then its spectral radius is at most the spectral radius of the n-vertex balanced complete k …