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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/2409.02593 |
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Table of Contents:
- Let $G = (V, E)$ be a graph. The first Zagreb index of a graph $G$ is defined as $\sum_{u \in V} d^2(u)$, where $d(u)$ is the degree of vertex $u$ in $G$. Using the Pólya-Szegő inequality, we in this paper present the first Zagreb index conditions for some Hamiltonian properties of a graph and an upper bound for the first Zagreb index of a graph.