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.
| Published in | Applied and Computational Mathematics (Volume 7, Issue 3) |
| DOI | 10.11648/j.acm.20180703.24 |
| Page(s) | 173-179 |
| Creative Commons |
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. |
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Copyright © The Author(s), 2018. Published by Science Publishing Group |
E-R Random Graph, General Distance Matrix, General Distance Energy, General Distance Estrada Index
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APA Style
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
ACS 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
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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Download@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://article.sciencepublishinggroup.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}
}
TY - JOUR T1 - General Distance Energies and General Distance Estrada Index of Random Graphs AU - Nan Gao Y1 - 2018/08/13 PY - 2018 N1 - https://doi.org/10.11648/j.acm.20180703.24 DO - 10.11648/j.acm.20180703.24 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 173 EP - 179 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20180703.24 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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