Abstract In 1990, Cvetković and Rowlinson conjectured that among all outerplanar graphs
on n vertices, K 1∨ P n− 1 attains the maximum spectral radius. In 2017, Tait and Tobin …

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 …

For a real number α∈[0, 1], the A α-matrix of a graph G is defined as A α (G)= α D (G)+(1− α)
A (G), where A (G) and D (G) are the adjacency matrix and diagonal degree matrix of G …

Given any real α∈[0, 1], the α-index of a graph G is the largest eigenvalue λ α (G) of the
matrix A α (G)= α D (G)+(1− α) A (G), where A (G) and D (G) stand for the adjacency matrix …

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 G be a simple undirected graph. For any real number α ∈ 0, 1 α∈ 0, 1, Nikiforov defined
the A_ α A α-matrix of G as A_ α (G)= α D (G)+(1-α) A (G) A α (G)= α D (G)+(1-α) A (G), where …

The A α matrix of a graph G is defined by Nikiforov as A α (G)= α D (G)+(1− α) A (G), where
α∈[0, 1], A (G) and D (G) respectively denotes the adjacency matrix and the degree …

Abstract Let G=(V (G), E (G)) be a simple undirected graph with vertex set V (G) and edge set
E (G). The cyclomatic number of a connected graph G is defined as θ (G)=| E (G)|−| V (G)|+ 1 …

The kth power of a graph G, denoted by G k, is a graph with the same set of vertices as G
such that two vertices are adjacent in G k if and only if their distance in G is at most k. In this …

Abstract Let A (G) and D (G) be the adjacency and degree matrices of a simple graph G on n
vertices, respectively. The A α-spectral radius of G is the largest eigenvalue of A α (G)= α D …