Lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg index
The Misbalance Rodeg (MR) index stands out among the 148 discrete Adriatic indices demonstrating considerable predictive capabilities in evaluations carried out by the International Academy of Mathematical Chemistry. This index excels particularly in forecasting both the enthalpy and the standard en...
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Elsevier
2025-01-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844024172660 |
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| author | Nasrin Dehgardi Mahdieh Azari Yilun Shang |
| author_facet | Nasrin Dehgardi Mahdieh Azari Yilun Shang |
| author_sort | Nasrin Dehgardi |
| collection | DOAJ |
| description | The Misbalance Rodeg (MR) index stands out among the 148 discrete Adriatic indices demonstrating considerable predictive capabilities in evaluations carried out by the International Academy of Mathematical Chemistry. This index excels particularly in forecasting both the enthalpy and the standard enthalpy of vaporization for octane isomers. Despite its significant chemical applicability, the MR index has not been extensively explored in the literature. One objective of this study is to highlight the importance of this graph invariant to the mathematical chemistry community by examining various mathematical properties associated with it. Our investigation specifically aims to ascertain the minimal values of the MR index for all trees and unicyclic graphs with a given order and maximum vertex degree. Additionally, we extend our analysis to molecular trees and provide a characterization of the respective minimal trees and unicyclic graphs. |
| format | Article |
| id | doaj-art-ac95fca12e0b4381921588b3f69e9653 |
| institution | Kabale University |
| issn | 2405-8440 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj-art-ac95fca12e0b4381921588b3f69e96532025-01-17T04:50:36ZengElsevierHeliyon2405-84402025-01-01111e41235Lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg indexNasrin Dehgardi0Mahdieh Azari1Yilun Shang2Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, IranDepartment of Mathematics, Kazerun Branch, Islamic Azad University, P. O. Box: 73135-168, Kazerun, Iran; Corresponding author.Department of Computer and Information Sciences, Northumbria University, Newcastle, NE1 8ST, UKThe Misbalance Rodeg (MR) index stands out among the 148 discrete Adriatic indices demonstrating considerable predictive capabilities in evaluations carried out by the International Academy of Mathematical Chemistry. This index excels particularly in forecasting both the enthalpy and the standard enthalpy of vaporization for octane isomers. Despite its significant chemical applicability, the MR index has not been extensively explored in the literature. One objective of this study is to highlight the importance of this graph invariant to the mathematical chemistry community by examining various mathematical properties associated with it. Our investigation specifically aims to ascertain the minimal values of the MR index for all trees and unicyclic graphs with a given order and maximum vertex degree. Additionally, we extend our analysis to molecular trees and provide a characterization of the respective minimal trees and unicyclic graphs.http://www.sciencedirect.com/science/article/pii/S2405844024172660Graph irregularityMisbalance rodeg indexTreesUnicyclic graphsSharp bounds |
| spellingShingle | Nasrin Dehgardi Mahdieh Azari Yilun Shang Lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg index Heliyon Graph irregularity Misbalance rodeg index Trees Unicyclic graphs Sharp bounds |
| title | Lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg index |
| title_full | Lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg index |
| title_fullStr | Lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg index |
| title_full_unstemmed | Lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg index |
| title_short | Lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg index |
| title_sort | lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg index |
| topic | Graph irregularity Misbalance rodeg index Trees Unicyclic graphs Sharp bounds |
| url | http://www.sciencedirect.com/science/article/pii/S2405844024172660 |
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