论文信息 - On unicyclic conjugated molecules with minimal energies

On unicyclic conjugated molecules with minimal energies

The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let U(k) be the set of all unicyclic graphs with a perfect matching. Let Cg(G) be the unique cycle of G with length g(G), and M(G) be a perfect matching of G. Let U0(k) be the subset of U(k) such that g(G)≡ 0 (mod 4), there are just g/2 independence edges of M(G) in Cg(G) and there are some edges of E(G)\ M(G) in G\ Cg(G) for any G∈U0(k). In this paper, we discuss the graphs with minimal and second minimal energies in U*(k) = U(k)\ U0(k), the graph with minimal energy in U0(k), and propose a conjecture on the graph with minimal energy in U(k).

Bo Zhou | Xueliang Li | Jianbin Zhang

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