The Effect of Vertex and Edge Removal on Sombor Index
A vertex degree based topological index called the Sombor index was recently defined in 2021 by Gutman and has been very popular amongst chemists and mathematicians. We determine the amount of change of the Sombor index when some elements are removed from a graph. This is done for several graph elem...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/16/2/170 |
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| author | Aysun Yurttas Gunes Hacer Ozden Ayna Ismail Naci Cangul |
| author_facet | Aysun Yurttas Gunes Hacer Ozden Ayna Ismail Naci Cangul |
| author_sort | Aysun Yurttas Gunes |
| collection | DOAJ |
| description | A vertex degree based topological index called the Sombor index was recently defined in 2021 by Gutman and has been very popular amongst chemists and mathematicians. We determine the amount of change of the Sombor index when some elements are removed from a graph. This is done for several graph elements, including a vertex, an edge, a cut vertex, a pendant edge, a pendant path, and a bridge in a simple graph. Also, pendant and non-pendant cases are studied. Using the obtained formulae successively, one can find the Sombor index of a large graph by means of the Sombor indices of smaller graphs that are just graphs obtained after removal of some vertices or edges. Sometimes, using iteration, one can manage to obtain a property of a really large graph in terms of the same property of many other subgraphs. Here, the calculations are made for a pendant and non-pendant vertex, a pendant and non-pendant edge, a pendant path, a bridge, a bridge path from a simple graph, and, finally, for a loop and a multiple edge from a non-simple graph. Using these results, the Sombor index of cyclic graphs and tadpole graphs are obtained. Finally, some Nordhaus–Gaddum type results are obtained for the Sombor index. |
| first_indexed | 2024-03-07T22:12:07Z |
| format | Article |
| id | doaj.art-7932c34202c845a4a467dd6e177498a9 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-07T22:12:07Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7932c34202c845a4a467dd6e177498a92024-02-23T15:35:55ZengMDPI AGSymmetry2073-89942024-02-0116217010.3390/sym16020170The Effect of Vertex and Edge Removal on Sombor IndexAysun Yurttas Gunes0Hacer Ozden Ayna1Ismail Naci Cangul2Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle Campus, Bursa 16059, TurkeyDepartment of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle Campus, Bursa 16059, TurkeyDepartment of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle Campus, Bursa 16059, TurkeyA vertex degree based topological index called the Sombor index was recently defined in 2021 by Gutman and has been very popular amongst chemists and mathematicians. We determine the amount of change of the Sombor index when some elements are removed from a graph. This is done for several graph elements, including a vertex, an edge, a cut vertex, a pendant edge, a pendant path, and a bridge in a simple graph. Also, pendant and non-pendant cases are studied. Using the obtained formulae successively, one can find the Sombor index of a large graph by means of the Sombor indices of smaller graphs that are just graphs obtained after removal of some vertices or edges. Sometimes, using iteration, one can manage to obtain a property of a really large graph in terms of the same property of many other subgraphs. Here, the calculations are made for a pendant and non-pendant vertex, a pendant and non-pendant edge, a pendant path, a bridge, a bridge path from a simple graph, and, finally, for a loop and a multiple edge from a non-simple graph. Using these results, the Sombor index of cyclic graphs and tadpole graphs are obtained. Finally, some Nordhaus–Gaddum type results are obtained for the Sombor index.https://www.mdpi.com/2073-8994/16/2/170Sombor indexvertex removaledge removalNordhaus–Gaddum type result |
| spellingShingle | Aysun Yurttas Gunes Hacer Ozden Ayna Ismail Naci Cangul The Effect of Vertex and Edge Removal on Sombor Index Symmetry Sombor index vertex removal edge removal Nordhaus–Gaddum type result |
| title | The Effect of Vertex and Edge Removal on Sombor Index |
| title_full | The Effect of Vertex and Edge Removal on Sombor Index |
| title_fullStr | The Effect of Vertex and Edge Removal on Sombor Index |
| title_full_unstemmed | The Effect of Vertex and Edge Removal on Sombor Index |
| title_short | The Effect of Vertex and Edge Removal on Sombor Index |
| title_sort | effect of vertex and edge removal on sombor index |
| topic | Sombor index vertex removal edge removal Nordhaus–Gaddum type result |
| url | https://www.mdpi.com/2073-8994/16/2/170 |
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