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On the Development and Application of Net-Sign Graph Theory

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Towards an Information Theory of Complex Networks

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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.

MSC2000 Primary 05C22, 05C40; Secondary 65S05, 94C15.

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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. Institüt für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074, Würzburg, Germany

    Prabhat K. Sahu

  2. Department of Chemistry and Biochemistry, National Chung Cheng University, Chia-Yi, 621, Taiwan

    Prabhat K. Sahu & Shyi-Long Lee

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  1. Prabhat K. Sahu
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Correspondence to Shyi-Long Lee .

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  1. Medizinische Informatik und Technik, Institute for Bioinformatics and Transla, UMIT-Private Universität für Gesundheits, Eduard Wallnöfer-Zentrum 1, Hall in Tirol, A-6060, Austria

    Matthias Dehmer

  2. Queen's University Belfast, School of Medicine, Dentistry, and Cell, Center for Cancer Research & Cell Biolog, Lisburn Road 97, Belfast, BT97BL, United Kingdom

    Frank Emmert-Streib

  3. Goethe-University Frankfurt am Main, Department of Philosophy and Historical, Center for Computing in the Humanities, Senckenberganlage 31, Frankfurt, 60325, Germany

    Alexander Mehler

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Sahu, P.K., Lee, SL. (2011). On the Development and Application of Net-Sign Graph Theory. In: Dehmer, M., Emmert-Streib, F., Mehler, A. (eds) Towards an Information Theory of Complex Networks. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4904-3_6

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