Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.14678 |
| Tags: |
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Sommario:
- 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.