Let G be a graph with adjacency matrix A (G) and let D (G) be the diagonal matrix of the
degrees of G. For any real α∈[0, 1], Nikiforov (2017)[7] defined the matrix A α (G) as A α (G) …

For any real α∈[0, 1], A α (G)= α D (G)+(1− α) A (G) is the A α-matrix of a graph G, where A
(G) is the adjacency matrix of G and D (G) is the diagonal matrix of the degrees of G. This …

The work of Wang et al.(2020) established an upper bound on the multiplicity of a real
number as an adjacency eigenvalue of an undirected simple graph G according to the …

Abstract In 2017, Nikiforov [12] proposed the A α-matrix of a graph G, which is defined as the
convex linear combination of the adjacency matrix A (G) and the diagonal matrix of degrees …

Let G be a graph with adjacency matrix A (G) and with D (G) the diagonal matrix of its vertex
degrees. Nikiforov defined the matrix A α (G), with α∈[0, 1], as A α (G)= α D (G)+(1− α) A (G) …

Let G be a graph with adjacency matrix A (G) and the degree diagonal matrix D (G). For any
real α∈[0, 1], Nikiforov (2017)[10] defined the matrix A α (G) as A α (G)= α D (G)+(1− α) A …

Let G be a graph on n vertices, its adjacency matrix and degree diagonal matrix are denoted
by A (G) and D (G), respectively. In 2017, Nikiforov [20] introduced the matrix A α (G)= α D …

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 graph of order n with m edges and chromatic number χ. Let A (G) be the
adjacency matrix and D (G) be the diagonal matrix of vertex degrees of G. Nikiforov defined …

For 0≤ α≤ 1, the A α-matrix of graph G is defined as A α (G)= α D (G)+(1− α) A (G), where D
(G) and A (G) are the diagonal matrix of the degrees and the adjacency matrix of G …