On tricyclic graphs of a given diameter with minimal energy

The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let G(n,d) be the class of tricyclic graphs G on n vertices with diameter d and containing no vertex disjoint odd cycles Cp,Cq of lengths p and q with p+q≡2(mod4). In this paper, we characterize the graphs with minimal energy in G(n,d).