Characterization of transmission irregular starlike and double starlike trees
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908395553947648 |
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| author | Damnjanović, Ivan |
| author_facet | Damnjanović, Ivan |
| contents | The transmission of a vertex in a connected graph is the sum of its distances to all the other vertices. A graph is transmission irregular (TI) when all of its vertices have mutually distinct transmissions. In an earlier paper, Al-Yakoob and Stevanović [Appl. Math. Comput. 380 (2020), 125257] gave the full characterization of TI starlike trees with three branches. Here, we improve these results by using a different approach to provide the complete characterization of all TI starlike trees. Moreover, we find the precise conditions under which a double starlike tree is TI. Finally, we implement the aforementioned conditions in order to find several infinite families of TI starlike trees and TI double starlike trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14259 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterization of transmission irregular starlike and double starlike trees Damnjanović, Ivan Combinatorics 05C12, 05C05, 05C75 The transmission of a vertex in a connected graph is the sum of its distances to all the other vertices. A graph is transmission irregular (TI) when all of its vertices have mutually distinct transmissions. In an earlier paper, Al-Yakoob and Stevanović [Appl. Math. Comput. 380 (2020), 125257] gave the full characterization of TI starlike trees with three branches. Here, we improve these results by using a different approach to provide the complete characterization of all TI starlike trees. Moreover, we find the precise conditions under which a double starlike tree is TI. Finally, we implement the aforementioned conditions in order to find several infinite families of TI starlike trees and TI double starlike trees. |
| title | Characterization of transmission irregular starlike and double starlike trees |
| topic | Combinatorics 05C12, 05C05, 05C75 |
| url | https://arxiv.org/abs/2311.14259 |