Energy ordering of catacondensed hexagonal systems

The energy of a graph G is defined as E(G)=∑i=1n|λi|, where λi (i=1,…,n) are the eigenvalues of G. In this work we define the coalescence of two graphs with respect to (oriented) edges, and show that for the graphs X and Y in Fig. 2, which are obtained by coalescence of bipartite graphs around the six-vertex cycle C6, E(X)⩾E(Y). As a by-product, we give energy ordering relations in the class of catacondensed hexagonal systems.