On the spectral radius of quasi-tree graphs

A connected graph G=(V,E) is called a quasi-tree, if there exists u0∈V(G) such that G-u0 is a tree. Denote Q(n,d0)={G:Gis a quasi-tree graph of ordernwithG-u0being a tree anddG(u0)=d0}. In this paper, we determined the maximal and the second maximal spectral radii of all quasi-tree graphs in the set Q(n,d0).