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Computing the Kirchhoff Index of Some xyz-Transformations of Regular Molecular Graphs

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Intelligent Computing Theory (ICIC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 8588))

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Abstract

Let G be a connected molecular graph. The resistance distance between any two vertices of G is defined as the effective resistance between the two corresponding nodes in the electrical network constructed from G by replacing each edge of Gwith a unit resistor. The Kirchhoff index of G is defined as the sum of resistance distances between all pairs of vertices. Gao et al. (2012) and You et al. (2013) gave formulae for the Kirchhoff index of two types of xyz – transformations, namely, the subdivision graph and the total graph, of regular graphs. In this paper, we compute the Kirchhoff index of some other xyz – transformations of regular (molecular) graphs, with explicit formulae for the Kirchhoff index of these transformation graphs being given in terms of parameters of the original graph.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, Shandong, 250100, P.R. China

    Yujun Yang

  2. School of Mathematics and Information Science, Yantai University, Yantai, Shandong, 264005, P.R. China

    Yujun Yang

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  1. Yujun Yang
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Editor information

Editors and Affiliations

  1. School of Electronics and Information Engineering, Tongji University, 4800 Caoan Road, 201804, Shanghai, China

    De-Shuang Huang

  2. Electrical and Electronics Department, Politecnico of Bari, Via Orabona, 4,, 70125, Bari, Italy

    Vitoantonio Bevilacqua

  3. School of Electrical, Computer and Telecommunications Engineering, University of Wollongon, 2522, North Wollongon, NSW, Australia

    Prashan Premaratne

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Yang, Y. (2014). Computing the Kirchhoff Index of Some xyz-Transformations of Regular Molecular Graphs. In: Huang, DS., Bevilacqua, V., Premaratne, P. (eds) Intelligent Computing Theory. ICIC 2014. Lecture Notes in Computer Science, vol 8588. Springer, Cham. https://doi.org/10.1007/978-3-319-09333-8_19

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  • DOI: https://doi.org/10.1007/978-3-319-09333-8_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09332-1

  • Online ISBN: 978-3-319-09333-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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