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The molecular graph Qn is obtained by attaching hexagons to the end vertices of the path graph Pn-12. Earlier empirical studies indicated that Qn has greatest energy among all bicyclic n-vertex (molecular) graphs. Recently, Li and Zhang proved that Qn has greatest energy among all bipartite bicyclic graphs, with the exception of the graphs Ra,b, a + b = n, where Ra,b is the graph obtained by joining the cycles Ca and Cb by an edge. This result is now com- pleted by showing that Qn has the greatest energy among all bipartite bicyclic n-vertex graphs.

Bicyclic molecular graphs with the greatest energy