Irregularity Measure of Graphs
A simple graph G is said to be regular if its vertices have the same number of neighbors. Otherwise, G is nonregular. So far, various formulas, such as the Albertson index, total Albertson index, and degree deviation, have been introduced to quantify the irregularity of a graph. In this paper, we pr...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/4891183 |
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| _version_ | 1849307686904004608 |
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| author | Ali Ghalavand Ivan Gutman Mostafa Tavakoli |
| author_facet | Ali Ghalavand Ivan Gutman Mostafa Tavakoli |
| author_sort | Ali Ghalavand |
| collection | DOAJ |
| description | A simple graph G is said to be regular if its vertices have the same number of neighbors. Otherwise, G is nonregular. So far, various formulas, such as the Albertson index, total Albertson index, and degree deviation, have been introduced to quantify the irregularity of a graph. In this paper, we present sharp lower bounds for these indices in terms of the order, size, maximum degree, minimum degree, and forgotten and Zagreb indices of the underlying graph. We also prove that if G has the minimum value of degree deviation, among all nonregular n,m-graphs, then ΔG−δG=1. |
| format | Article |
| id | doaj-art-21b54c0d93224c89895b8300ca9a4749 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-21b54c0d93224c89895b8300ca9a47492025-08-20T03:54:42ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/4891183Irregularity Measure of GraphsAli Ghalavand0Ivan Gutman1Mostafa Tavakoli2Department of Applied MathematicsFaculty of ScienceDepartment of Applied MathematicsA simple graph G is said to be regular if its vertices have the same number of neighbors. Otherwise, G is nonregular. So far, various formulas, such as the Albertson index, total Albertson index, and degree deviation, have been introduced to quantify the irregularity of a graph. In this paper, we present sharp lower bounds for these indices in terms of the order, size, maximum degree, minimum degree, and forgotten and Zagreb indices of the underlying graph. We also prove that if G has the minimum value of degree deviation, among all nonregular n,m-graphs, then ΔG−δG=1.http://dx.doi.org/10.1155/2023/4891183 |
| spellingShingle | Ali Ghalavand Ivan Gutman Mostafa Tavakoli Irregularity Measure of Graphs Journal of Mathematics |
| title | Irregularity Measure of Graphs |
| title_full | Irregularity Measure of Graphs |
| title_fullStr | Irregularity Measure of Graphs |
| title_full_unstemmed | Irregularity Measure of Graphs |
| title_short | Irregularity Measure of Graphs |
| title_sort | irregularity measure of graphs |
| url | http://dx.doi.org/10.1155/2023/4891183 |
| work_keys_str_mv | AT alighalavand irregularitymeasureofgraphs AT ivangutman irregularitymeasureofgraphs AT mostafatavakoli irregularitymeasureofgraphs |