On the Development and Application of Net-Sign Graph Theory

Chapter

Abstract

This report briefly describes the development and applications of net-sign graph theory. The current work enunciates the graph (molecule) signature of non-alternant non-benzenoid hydrocarbons with odd member of rings (non-bipartite molecular graphs) based on chemical signed graph theory. Experimental evidences and Hückel spectrum reveal that structure possessing nonbonding molecular orbital (NBMOs) is very unstable and highly reactive under the drastic conditions of low temperature. Chemical signed graph theoretical approach is applied successfully to classify the non-bipartite molecular graphs with a view to Randic’s conjugated circuit models based on their spectral characteristic. The obtained results based on net-sign approach are compared with those obtained using Hückel calculations.

Keywords

Net-sign graphs Non-bipartite molecular graphs Spectral characteristic 

Notes

Acknowledgements

We are thankful to Milan Randic for his suggestions. This research is supported by National Science Council, Taiwan.

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Authors and Affiliations

  1. 1.Institüt für Physikalische und Theoretische ChemieUniversität WürzburgWürzburgGermany
  2. 2.Department of Chemistry and BiochemistryNational Chung Cheng UniversityChia-YiTaiwan

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