On bicyclic graphs with maximal energy

Abstract: Let be the eigenvalues of a graph of order . The energy of is defined as . Let be the graph obtained from two copies of joined by a path , be the class of all bipartite bicyclic graphs that are not the graph obtained from two cycles and ( and (mod 4)) joined by an edge. In this paper, we show that is the graph with maximal energy in , which gives a partial solution to Gutman’s conjecture in Gutman and Vidović (2001) [I. Gutman, D. Vidović, Quest for molecular graphs with maximal energy: a computer experiment, J. Chem. Inf. Sci. 41 (2001) 1002–1005]. [Copyright &y& Elsevier]