Let M be a partitioned matrix and B be its equitable quotient matrix. In this paper, we prove
the inclusion of their spectra σ (B)⊆ σ (M), and the equality of their spectral radii ρ (B)= ρ (M) …

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 D be a digraph of order n and let A (D) be the adjacency matrix of D. Let D eg (D) be the
diagonal matrix of vertex out-degrees of D. For any real α∈[0, 1], the generalized adjacency …

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 strongly connected digraph and α∈[0, 1]. In Liu et al.(2019)[13] the matrix A α
(D)= α D eg (D)+(1− α) A (D), where A (D) and D eg (D) are the adjacency matrix and the …

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 …

Let D be a digraph of order n and let A (D) be the adjacency matrix of D. Let Deg (D) be the
diagonal matrix of vertex out-degrees of D. For any real α∈[0, 1], the generalized adjacency …

Let G‾ n, k denote the set of strongly connected digraphs with order n and arc connectivity k,
and let G‾ n, k⁎ denote the set of digraphs in G‾ n, k with all vertices having outdegree and …