A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two. Let J(n)(g) is 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 J(n)(g) with exactly three (resp. four) cycles. Furthermore, the upper bound of the Laplacian spectral radius and the extremal gr...
