Computing Energy and Some Topological Indices of <img width="60" height="43" src="http://article.sciencepublishinggroup.com/journal/247/2470989/image001.gif" />

Mohammad Javad Nikmehr; Najmeh Soleimani

doi:doi:10.11648/j.mcs.20160104.15

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Computing Energy and Some Topological Indices of

Mohammad Javad Nikmehr, Najmeh Soleimani

Published in Mathematics and Computer Science (Volume 1, Issue 4)

Received: 3 September 2016 Accepted: 16 November 2016 Published: 20 December 2016

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Abstract

For a commutative ring , the total graph of which denoted by , is a graph with all elements of R as vertices, and two distinct vertices are adjacent if and only if , where denotes the set of zero-divisors of R. In an earlier study, we computed Wiener, hyper-Wiener, reverse Wiener, Randic ́, Zagreb, and indices of zero-divisor graph. In this study, some computer programs are prepared to calculate the zero-divisors and adjacency matrix of the given graph which, apply these programs to compute the energy and first edge-Wiener, sum-connectivity, harmonic, augmented Zagreb and hyper-Zagreb indices.

Published in	Mathematics and Computer Science (Volume 1, Issue 4)
DOI	10.11648/j.mcs.20160104.15
Page(s)	101-107
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.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Ring, Zero-Divisor Graph, MATLAB Program, Energy, Topological Indices

References

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[2]	Dos ̌lic ́, T. and Saheli, M. "Augmented eccentric connectivity index of single defect nanocones." Journal of mathematical nanoscience. Vol. 1, No. 1, 2011, pp. 25-31.
[3]	Heydari, A. and Taeri, B. "Wiener and Schultz indices of TUC_4 C_8 (S) nanotubes." MATCH Communications in Mathematical and in Computer Chemistry. Vol. 57, 2007, pp. 665-676.
[4]	Nikmehr, M. J., Soleimani, N. and Tavallaee, H. A. "Computing some topological indices of carbon nanotubes." Proceedings of the Institute of Applied Mathematics. Vol. 4, No. 1, 2015, pp. 20-25.
[5]	Soleimani, N., Nikmehr, M. J. and Tavallaee, H. A. "Theoretical study of nanostructures using topological indices." Studia Universitatis Babes-Bolyai, Chemia. Vol. 59, No. 4, 2014, pp. 139-148.
[6]	Soleimani, N., Nikmehr, M. J. and Tavallaee, H. A. "Computation of the different topological indices of nanostructures." Journal of the national science foundation of Sri Lanka. Vol. 43, No. 2, 2015, pp. 127-133.
[7]	Soleimani, N., Mohseni, E. and Maleki, N. "Connectivity indices of some famous dendrimers." Journal of Chemical and Pharmaceutical Research. Vol. 8, No. 8, 2016, pp. 229-235.
[8]	Nikmehr, M. J., Heidarzadeh, L. and Soleimani, N. "Calculating different topological indices of total graph of Z_n." Studia Scientiarum Mathematicarum Hungarica. Vol. 51, No. 1, 2014, pp. 133-140.
[9]	Gutman, I. and Polansky, O. E. "Mathematical Concepts in Organic Chemistry." Springer-Verlag, Berlin. 1986.
[10]	Gutman, I. "The energy of a graph: old and new results." in Algebraic Combinatorics and Applications, Betten A., Kohner, R. Laue A. & Wassermann A., eds., Springer, Berlin. 2001, pp. 196-211.
[11]	Wiener, H. "Structural determination of the paraffin boiling points." Journal of the American Chemical Society. Vol. 69, 1947, pp. 17-20
[12]	Iranmanesh, A., Gutman, I., Khormali, O. and Mahmiani, A. "The edge versions of the Wiener index." MATCH Communications in Mathematical and in Computer Chemistry. Vol. 61, 2009, pp. 663-672.
[13]	Zhou, B. and Trinajstić, N. "On a novel connectivity index." Journal of Mathematical Chemistry. Vol. 46, 2009, pp. 1252-1270.
[14]	Fajtlowicz, S. "On conjectures of Graffiti-II." Congr. Numer. Vol. 60, 1987, pp. 187-197.
[15]	Furtula, B., Graovac, A. and Vukičević, D. "Augmented Zagreb index." Journal of Mathematical Chemistry. Vol. 48, 2010, pp. 370-380.
[16]	Shirdel, G. H., Rezapour, H. and Sayadi, A. M. "The Hyper-Zagreb index of graph operations." Iranian Journal of Mathematical Chemistry. Vol. 4, No. 2, 2013, pp. 213-220.
[17]	Maimani, H. R., Wickham, C. and Yassemi, S. "Rings whose total graphs have genus at most one." Rocky Mountain Journal of Mathematics. Vol. 42, No. 5, 2012, pp. 1551-1560.
[18]	Caporossi, G., Cvetković, D., Gutman, I and Hansen, P. "Variable neighborhood search for extremal graphs. 2. Finding graphs with external energy." Journal of Chemical Information and Computer Sciences. Vol. 39, 1999, pp. 984-996.

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Mohammad Javad Nikmehr, Najmeh Soleimani. (2016). Computing Energy and Some Topological Indices of . Mathematics and Computer Science, 1(4), 101-107. https://doi.org/10.11648/j.mcs.20160104.15

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ACS Style

Mohammad Javad Nikmehr; Najmeh Soleimani. Computing Energy and Some Topological Indices of . Math. Comput. Sci. 2016, 1(4), 101-107. doi: 10.11648/j.mcs.20160104.15

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AMA Style

Mohammad Javad Nikmehr, Najmeh Soleimani. Computing Energy and Some Topological Indices of . Math Comput Sci. 2016;1(4):101-107. doi: 10.11648/j.mcs.20160104.15

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@article{10.11648/j.mcs.20160104.15,
  author = {Mohammad Javad Nikmehr and Najmeh Soleimani},
  title = {Computing Energy and Some Topological Indices of },
  journal = {Mathematics and Computer Science},
  volume = {1},
  number = {4},
  pages = {101-107},
  doi = {10.11648/j.mcs.20160104.15},
  url = {https://doi.org/10.11648/j.mcs.20160104.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20160104.15},
  abstract = {For a commutative ring , the total graph of  which denoted by , is a graph with all elements of R as vertices, and two distinct vertices  are adjacent if and only if , where  denotes the set of zero-divisors of R. In an earlier study, we computed Wiener, hyper-Wiener, reverse Wiener, Randic ́, Zagreb,  and  indices of zero-divisor graph. In this study, some computer programs are prepared to calculate the zero-divisors and adjacency matrix of the given graph which, apply these programs to compute the energy and first edge-Wiener, sum-connectivity, harmonic, augmented Zagreb and hyper-Zagreb indices.},
 year = {2016}
}

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TY  - JOUR
T1  - Computing Energy and Some Topological Indices of 
AU  - Mohammad Javad Nikmehr
AU  - Najmeh Soleimani
Y1  - 2016/12/20
PY  - 2016
N1  - https://doi.org/10.11648/j.mcs.20160104.15
DO  - 10.11648/j.mcs.20160104.15
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 101
EP  - 107
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20160104.15
AB  - For a commutative ring , the total graph of  which denoted by , is a graph with all elements of R as vertices, and two distinct vertices  are adjacent if and only if , where  denotes the set of zero-divisors of R. In an earlier study, we computed Wiener, hyper-Wiener, reverse Wiener, Randic ́, Zagreb,  and  indices of zero-divisor graph. In this study, some computer programs are prepared to calculate the zero-divisors and adjacency matrix of the given graph which, apply these programs to compute the energy and first edge-Wiener, sum-connectivity, harmonic, augmented Zagreb and hyper-Zagreb indices.
VL  - 1
IS  - 4
ER  -

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Author Information

Mohammad Javad Nikmehr

Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
Najmeh Soleimani

Young Researchers and Elite Club, Karj Branch, Islamic Azad University, Karaj, Iran

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APA Style

Mohammad Javad Nikmehr, Najmeh Soleimani. (2016). Computing Energy and Some Topological Indices of . Mathematics and Computer Science, 1(4), 101-107. https://doi.org/10.11648/j.mcs.20160104.15

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ACS Style

Mohammad Javad Nikmehr; Najmeh Soleimani. Computing Energy and Some Topological Indices of . Math. Comput. Sci. 2016, 1(4), 101-107. doi: 10.11648/j.mcs.20160104.15

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AMA Style

Mohammad Javad Nikmehr, Najmeh Soleimani. Computing Energy and Some Topological Indices of . Math Comput Sci. 2016;1(4):101-107. doi: 10.11648/j.mcs.20160104.15

Copy | Download

@article{10.11648/j.mcs.20160104.15,
  author = {Mohammad Javad Nikmehr and Najmeh Soleimani},
  title = {Computing Energy and Some Topological Indices of },
  journal = {Mathematics and Computer Science},
  volume = {1},
  number = {4},
  pages = {101-107},
  doi = {10.11648/j.mcs.20160104.15},
  url = {https://doi.org/10.11648/j.mcs.20160104.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20160104.15},
  abstract = {For a commutative ring , the total graph of  which denoted by , is a graph with all elements of R as vertices, and two distinct vertices  are adjacent if and only if , where  denotes the set of zero-divisors of R. In an earlier study, we computed Wiener, hyper-Wiener, reverse Wiener, Randic ́, Zagreb,  and  indices of zero-divisor graph. In this study, some computer programs are prepared to calculate the zero-divisors and adjacency matrix of the given graph which, apply these programs to compute the energy and first edge-Wiener, sum-connectivity, harmonic, augmented Zagreb and hyper-Zagreb indices.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Computing Energy and Some Topological Indices of 
AU  - Mohammad Javad Nikmehr
AU  - Najmeh Soleimani
Y1  - 2016/12/20
PY  - 2016
N1  - https://doi.org/10.11648/j.mcs.20160104.15
DO  - 10.11648/j.mcs.20160104.15
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 101
EP  - 107
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20160104.15
AB  - For a commutative ring , the total graph of  which denoted by , is a graph with all elements of R as vertices, and two distinct vertices  are adjacent if and only if , where  denotes the set of zero-divisors of R. In an earlier study, we computed Wiener, hyper-Wiener, reverse Wiener, Randic ́, Zagreb,  and  indices of zero-divisor graph. In this study, some computer programs are prepared to calculate the zero-divisors and adjacency matrix of the given graph which, apply these programs to compute the energy and first edge-Wiener, sum-connectivity, harmonic, augmented Zagreb and hyper-Zagreb indices.
VL  - 1
IS  - 4
ER  -

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