On unicyclic conjugated molecules with minimal energies

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• 作者：Xueliang Li ; Jianbin Zhang and Bo Zhou
• 关键词：energy ; unicyclic graph ; characteristic polynomial ; eigenvalue ; perfect matching
• 刊名：Journal of Mathematical Chemistry
• 出版年：2007
• 出版时间：November, 2007
• 年：2007
• 卷：42
• 期：4
• 页码：729-740
• 全文大小：144 KB
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistry
  Physical Chemistry
  Theoretical and Computational Chemistry
  Mathematical Applications in Chemistry
  
• 出版者：Springer Netherlands
• ISSN：1572-8897

文摘

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 C _g(G) be the unique cycle of G with length g(G), and M(G) be a perfect matching of G. Let U 0(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 C _g(G) and there are some edges of E(G)\ M(G) in G\ C _g(G) for any G∈U 0(k). In this paper, we discuss the graphs with minimal and second minimal energies in U *(k) = U(k)\ U 0(k), the graph with minimal energy in U 0(k), and propose a conjecture on the graph with minimal energy in U(k).