BOUNDING THE Aα-SPECTRAL RADIUS OF k-CONNECTED IRREGULAR GRAPHS

Let G be a simple graph of order n. For alpha is an element of[0,1], the A(alpha)-matrix of G is defined as A(alpha)= alpha D(G)+(1- alpha) A(G), where A(G) and D(G) are the adjacency matrix and the diagonal matrix of vertex degrees of G, respectively. The largest eigenvalue of A(alpha)(G), denoted by rho(alpha)(G), is called the A(alpha) spectral radius of G. We give an upper bound on rho(alpha)(G) for k-connected irregular graphs. Moreover, we also derive an upper bound on rho(alpha)(G) when G is a subgraph of a k-connected regular graph. Our results improve or extend the existing results, respectively.