Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order

摘要

For every integer n >= 4, it is proved that there is a unique graph of order n which maximizes the spectral radius of the unoriented Laplacian matrix over all bicyclic graphs of order n, namely, the graph obtained from the cycle C-4 by first adding a chord and then attaching n-4 pendant edges to one end of the chord.