Bicyclic molecular graphs with the greatest energy

Abstract

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 completed by showing that Qn has the greatest energy among all bipartite bicyclic n-vertex graphs.