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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2309.12682 |
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| _version_ | 1866913688742526976 |
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| author | Pan, Xiangrui Zeng, Cheng Li, Longyu Li, Gengji |
| author_facet | Pan, Xiangrui Zeng, Cheng Li, Longyu Li, Gengji |
| contents | In this paper, we focus on comparing the first and second Zagreb-Fermat eccentricity indices of graphs. We show that $$\frac{\sum_{uv\in E\left( G \right)}{\varepsilon_3\left( u \right) \varepsilon_3\left( v \right)}}{m\left( G \right)} \leq \frac{\sum_{u\in V\left( G \right)}{\varepsilon_{3}^{2}\left( u \right)}}{n\left( G \right)} $$ holds for all acyclic and unicyclic graphs. Besides, we verify that the inequality may not be applied to graphs with at least two cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12682 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The comparison of two Zagreb-Fermat eccentricity indices Pan, Xiangrui Zeng, Cheng Li, Longyu Li, Gengji Combinatorics In this paper, we focus on comparing the first and second Zagreb-Fermat eccentricity indices of graphs. We show that $$\frac{\sum_{uv\in E\left( G \right)}{\varepsilon_3\left( u \right) \varepsilon_3\left( v \right)}}{m\left( G \right)} \leq \frac{\sum_{u\in V\left( G \right)}{\varepsilon_{3}^{2}\left( u \right)}}{n\left( G \right)} $$ holds for all acyclic and unicyclic graphs. Besides, we verify that the inequality may not be applied to graphs with at least two cycles. |
| title | The comparison of two Zagreb-Fermat eccentricity indices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2309.12682 |