Applied and Computational Mathematics

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General Distance Energies and General Distance Estrada Index of Random Graphs

Received: 09 August 2018    Accepted:     Published: 13 August 2018
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Abstract

In 2000s, Gutman and Güngör introduced the concept of distance energy and the distance Estrada index for a simple graph G respectively. Moreover, many researchers established a large number of upper and lower bounds for these two invariants. But there are only a few graphs attaining the equalities of those bounds. In this paper, however, the exact estimates to general distance energy are formulated for almost all graphs by probabilistic and algebraic approaches. The bounds to general distance Estrada index are also established for almost all graphs by probabilistic and algebraic approaches. The results of this paper generalize the results of the distance energy and distance Estrada of random graph.

DOI 10.11648/j.acm.20180703.24
Published in Applied and Computational Mathematics (Volume 7, Issue 3, June 2018)
Page(s) 173-179
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

E-R Random Graph, General Distance Matrix, General Distance Energy, General Distance Estrada Index

References
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[8] Gutman I. The Energy of a Graph: Old and New Results [M]// Algebraic Combinatorics and Applications. Springer Berlin Heidelberg, 2001, pp.196-211.
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[19] R. Carbó–Dorca, Smooth fuction topological structure descriptors based on graph-spectra, J. Math. Chem. 44 (2008), pp: 373–378.
[20] A. D. Güngör, Ş. B. Bozkurt, On the distance Estrada index of graphs, Hacettepe J. Math. Stat., 38 (2009), pp.277–283.
[21] Ş. B. Bozkurt, D. Bozkurt, Bounds for the distance Estrada index of graphs. AIP Conf. Proc., 1648 (2015), pp. 1351–1359.
[22] Güngör A D, Sinan A. On the Harary energy and Harary Estrada index of a graph. MATCH Commun. Math. Comput. Chem., 64 (2010), pp: 270-285.
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  • College of Science, Xi'an Shiyou University, Xi'an, China

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    Nan Gao. (2018). General Distance Energies and General Distance Estrada Index of Random Graphs. Applied and Computational Mathematics, 7(3), 173-179. https://doi.org/10.11648/j.acm.20180703.24

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    Nan Gao. General Distance Energies and General Distance Estrada Index of Random Graphs. Appl. Comput. Math. 2018, 7(3), 173-179. doi: 10.11648/j.acm.20180703.24

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    AMA Style

    Nan Gao. General Distance Energies and General Distance Estrada Index of Random Graphs. Appl Comput Math. 2018;7(3):173-179. doi: 10.11648/j.acm.20180703.24

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  • @article{10.11648/j.acm.20180703.24,
      author = {Nan Gao},
      title = {General Distance Energies and General Distance Estrada Index of Random Graphs},
      journal = {Applied and Computational Mathematics},
      volume = {7},
      number = {3},
      pages = {173-179},
      doi = {10.11648/j.acm.20180703.24},
      url = {https://doi.org/10.11648/j.acm.20180703.24},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20180703.24},
      abstract = {In 2000s, Gutman and Güngör introduced the concept of distance energy and the distance Estrada index for a simple graph G respectively. Moreover, many researchers established a large number of upper and lower bounds for these two invariants. But there are only a few graphs attaining the equalities of those bounds. In this paper, however, the exact estimates to general distance energy are formulated for almost all graphs by probabilistic and algebraic approaches. The bounds to general distance Estrada index are also established for almost all graphs by probabilistic and algebraic approaches. The results of this paper generalize the results of the distance energy and distance Estrada of random graph.},
     year = {2018}
    }
    

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    AU  - Nan Gao
    Y1  - 2018/08/13
    PY  - 2018
    N1  - https://doi.org/10.11648/j.acm.20180703.24
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    AB  - In 2000s, Gutman and Güngör introduced the concept of distance energy and the distance Estrada index for a simple graph G respectively. Moreover, many researchers established a large number of upper and lower bounds for these two invariants. But there are only a few graphs attaining the equalities of those bounds. In this paper, however, the exact estimates to general distance energy are formulated for almost all graphs by probabilistic and algebraic approaches. The bounds to general distance Estrada index are also established for almost all graphs by probabilistic and algebraic approaches. The results of this paper generalize the results of the distance energy and distance Estrada of random graph.
    VL  - 7
    IS  - 3
    ER  - 

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