Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights
The graph entropy was proposed by Körner in the year 1973 when he was studying the problem of coding in information theory. The foundation of graph entropy is in information theory, but it was demonstrated to be firmly identified with some established and often examined graph-theoretic ideas. For in...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/3562382 |
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| author | Yujie Huang Hafiz Mutee-ur-Rehman Saima Nazeer Deeba Afzal Xiaoli Qiang |
| author_facet | Yujie Huang Hafiz Mutee-ur-Rehman Saima Nazeer Deeba Afzal Xiaoli Qiang |
| author_sort | Yujie Huang |
| collection | DOAJ |
| description | The graph entropy was proposed by Körner in the year 1973 when he was studying the problem of coding in information theory. The foundation of graph entropy is in information theory, but it was demonstrated to be firmly identified with some established and often examined graph-theoretic ideas. For instance, it gives an equal definition to a graph to be flawless, and it can likewise be connected to acquire lower bounds in graph covering problems. The objective of this study is to solve the open problem suggested by Kwun et al. in 2018. In this paper, we study the weighted graph entropy by taking augmented Zagreb edge weight and give bounds of it for regular, connected, bipartite, chemical, unicyclic, etc., graphs. Moreover, we compute the weighted graph entropy of certain nanotubes and plot our results to see dependence of weighted entropy on involved parameters. |
| format | Article |
| id | doaj-art-c9e8aa17ae3b41d8820d3e85f9adba4b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-c9e8aa17ae3b41d8820d3e85f9adba4b2025-02-03T06:46:39ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/35623823562382Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge WeightsYujie Huang0Hafiz Mutee-ur-Rehman1Saima Nazeer2Deeba Afzal3Xiaoli Qiang4Sichuan University, Jinjiang College, Meishan 620860, ChinaDepartment of Mathematics and Statistics, The University of Lahore, Lahore 54000, PakistanDepartment of Mathematics, Lahore College for Women University, Lahore 54000, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Lahore 54000, PakistanInstitute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaThe graph entropy was proposed by Körner in the year 1973 when he was studying the problem of coding in information theory. The foundation of graph entropy is in information theory, but it was demonstrated to be firmly identified with some established and often examined graph-theoretic ideas. For instance, it gives an equal definition to a graph to be flawless, and it can likewise be connected to acquire lower bounds in graph covering problems. The objective of this study is to solve the open problem suggested by Kwun et al. in 2018. In this paper, we study the weighted graph entropy by taking augmented Zagreb edge weight and give bounds of it for regular, connected, bipartite, chemical, unicyclic, etc., graphs. Moreover, we compute the weighted graph entropy of certain nanotubes and plot our results to see dependence of weighted entropy on involved parameters.http://dx.doi.org/10.1155/2020/3562382 |
| spellingShingle | Yujie Huang Hafiz Mutee-ur-Rehman Saima Nazeer Deeba Afzal Xiaoli Qiang Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights Discrete Dynamics in Nature and Society |
| title | Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights |
| title_full | Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights |
| title_fullStr | Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights |
| title_full_unstemmed | Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights |
| title_short | Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights |
| title_sort | some bounds of weighted entropies with augmented zagreb index edge weights |
| url | http://dx.doi.org/10.1155/2020/3562382 |
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