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Some results on energy of unicyclic graphs with n vertices

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Abstract

A unicyclic graph is a connected graph whose number of edges is equal to the number of vertices. Hou (J Math Chem 29:163–168, 2001) first considered the minimal energy for general unicyclic graphs. In this paper, we determine the unicyclic graphs with the minimal energy in \({\mathcal {U}_n^l}\) and the unicyclic graphs with the first forth smallest energy in \({\mathcal {U}_n\,(n\geq 13)}\) vertices.

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References

  1. Cvetkoić D., Doob M., Sachs H.: Spectra of Graphs Theory and Applications. Academic Press, New York (1980)

    Google Scholar 

  2. Gutman I.: Acyclic systems with extremal Hückel π-electron energy. Theor. Chem. Acta (Berl.) 45, 79–87 (1977)

    Article  CAS  Google Scholar 

  3. I. Gutman, in Algebraic Combinatorics and Applications, ed. by A. Betten, A. Kohnert, R. Laue, A. Wassermann (Springer, Berlin, 2001), pp. 196–211

  4. Gutman I.: Topology and stability of conjugated hydrocarbons: the dependence of total π-electron energy on molecular topology. J. Serb. Chem. Soc. 70, 441–456 (2005)

    Article  CAS  Google Scholar 

  5. Gutman I., Polansky O.E.: Mathematical Concepts in Organic Chemistry. Springer, Berlin (1986)

    Google Scholar 

  6. Hou Y.: Unicyclic graphs with the minimal energy. J. Math. Chem. 29, 163–168 (2001)

    Article  CAS  Google Scholar 

  7. Li S., Li N.: On minimal energies of trees with given diameter. Electron. J. Linear Algebra 17, 414–425 (2008)

    CAS  Google Scholar 

  8. Li X., Zhang J., Zhou B.: On unicyclic conjugated molecules with the minimal energies. J. Math. Chem. 42(4), 729–740 (2007)

    Article  CAS  Google Scholar 

  9. Wang W., Chang A., Lu D.: Unicyclic graphs possessing Kekuké structures with minimal energy. J. Math. Chem. 42(3), 311–320 (2007)

    Article  CAS  Google Scholar 

  10. Ye L., Yuan X.: On the minimal energy of trees with a given number number of pendent vertices. MATCH Commun. Math. Comput. Chem. 54(1), 193–201 (2007)

    Google Scholar 

  11. Zhang F., Li H.: On acyclic conjugated molecules with minimal energies. Discrete Appl. Math. 92, 71–84 (1999)

    Article  Google Scholar 

Download references

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Correspondence to Ying Liu.

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Liu, Y. Some results on energy of unicyclic graphs with n vertices. J Math Chem 47, 1–10 (2010). https://doi.org/10.1007/s10910-009-9528-2

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  • DOI: https://doi.org/10.1007/s10910-009-9528-2

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