The laplacian spectral radius of tricyclic graphs with a given girth - Wang, Chengyong; Li, Shuchao; Yan, Lixia (Utilitas Mathematica, 2013)
A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two. Let ng be the class of all n-vertex tricyclic graphs with girth g. This paper determines the unique graph with the maximal Laplacian spectral radius among all graphs in ng with exactly three (resp. four) cycles. Furthermore, the upper bound of the Laplacian spectral radius and the extremal graph in ng are also obtained, where g is even.