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 |
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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. |
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Ring, Zero-Divisor Graph, MATLAB Program, Energy, Topological Indices
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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
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
@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} }
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 -