Let G be a graph with n vertices, and let A (G) and D (G) denote respectively the adjacency
matrix and the degree matrix of G. Define A α (G)= α D (G)+(1− α) A (G) for any real α∈[0, 1] …

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 …

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 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 …

Let G be a connected graph with distance matrix D (G), and let T r (G) be the diagonal matrix
of vertex transmissions of G. For any α∈[0, 1], the D α-matrix of G is defined as D α (G)= α T r …

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 …

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

Abstract Let α∈[0, 1), and let G be a graph of even order n with n≥ f (α), where f (α)= 10 for
0≤ α≤ 1/2, f (α)= 14 for 1/2< α≤ 2/3 and f (α)= 5/(1− α) for 2/3< α< 1. In this paper, it is …

Let G be an n-vertex graph. A matching in G is a set of independent edges, ie, no two edges
in the set are adjacent in G. The matching number is the maximal size of a matching in G …