On tricyclic graphs of a given diameter with minimal energy

Abstract 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 C p , C q of lengths p and q with p + q ≡ 2 ( mod 4 ) . In this paper, we characterize the graphs with minimal energy in G ( n , d ) .