Upper bounds on the spectral radius of book-free and/or K2,l-free graphs Original Research Article

The spectral radius ρ(G) of a graph G is the largest eigenvalue of its adjacency matrix. Let Bk denote a book with k . In this paper, we generalize a result of Lu et al [M. Lu, H. Liu, F. Tian, A new upper bound for the spectral radius of graphs with girth at least 5, Linear Algebra Appl. 414 (2006) 512–516.] on the upper bound for the spectral radius of connected graphs with girth at least 5 to connected {Bk+1,K2,l+1}-free graphs G of order n with maximum degree Δ as follows:imagewith equality if and only if G is a strongly regular graph with parameters (Δ,k,l). This implies sharp upper bounds for book-free or K2,l-free graphs.