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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.13403 |
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| _version_ | 1866914687652724736 |
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| author | Gerbner, Dániel |
| author_facet | Gerbner, Dániel |
| contents | Xu in 2011 determined the largest value of the second Zagreb index in an $n$-vertex graph $G$ with clique number $k$, and also the smallest value with the additional assumption that $G$ is connected. We extend these results to other degree-based topological indices. The key property of the clique number in the first result is that $G$ is $K_{k+1}$-free, while the key property in the second result is that $G$ contains a $K_{k+1}$. We also extend our investigations to other forbidden/prescribed subgraphs. Our main tool is showing that several degree-based topological indices are equal to the weighted sum of the number of some subgraphs of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13403 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On extremal values of some degree-based topological indices with a forbidden or a prescribed subgraph Gerbner, Dániel Combinatorics Xu in 2011 determined the largest value of the second Zagreb index in an $n$-vertex graph $G$ with clique number $k$, and also the smallest value with the additional assumption that $G$ is connected. We extend these results to other degree-based topological indices. The key property of the clique number in the first result is that $G$ is $K_{k+1}$-free, while the key property in the second result is that $G$ contains a $K_{k+1}$. We also extend our investigations to other forbidden/prescribed subgraphs. Our main tool is showing that several degree-based topological indices are equal to the weighted sum of the number of some subgraphs of $G$. |
| title | On extremal values of some degree-based topological indices with a forbidden or a prescribed subgraph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.13403 |