New improved lower bounds for Zagreb indices of graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911112148025344 |
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| author | Verma, Mamta Kumar, Ravinder |
| author_facet | Verma, Mamta Kumar, Ravinder |
| contents | This paper presents new lower bounds for the first general Zagreb index $Z_α(G)$ involving two, three, and four arbitrary degrees of vertices of a simple graph $G$. For the special cases $α= 2$ and $α= -2$, the results give sharper bounds for the first Zagreb index $M_1(G)$ and the modified first Zagreb index ${}^{m}M_1(G)$, thereby improving several well-known inequalities in the literature. Furthermore, some applications of the derived bounds for $M_1(G)$ are demonstrated, establishing new bounds for the second Zagreb index, the spectral radius, Nordhaus-Gaddum type bounds, and their corresponding coindices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New improved lower bounds for Zagreb indices of graphs Verma, Mamta Kumar, Ravinder Combinatorics This paper presents new lower bounds for the first general Zagreb index $Z_α(G)$ involving two, three, and four arbitrary degrees of vertices of a simple graph $G$. For the special cases $α= 2$ and $α= -2$, the results give sharper bounds for the first Zagreb index $M_1(G)$ and the modified first Zagreb index ${}^{m}M_1(G)$, thereby improving several well-known inequalities in the literature. Furthermore, some applications of the derived bounds for $M_1(G)$ are demonstrated, establishing new bounds for the second Zagreb index, the spectral radius, Nordhaus-Gaddum type bounds, and their corresponding coindices. |
| title | New improved lower bounds for Zagreb indices of graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.14678 |