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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.00798 |
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Table of Contents:
- Let $ G $ be a simple graph with the vertex cover number $ τ$. The energy $ \mathcal{E}(G) $ of $ G $ is the sum of the absolute values of all the adjacency eigenvalues of $ G $. In this article, we establish $ \mathcal{E}(G)\geq 2τ$ for several classes of graphs. The result significantly improves the known result $ \mathcal{E}(G)\geq 2τ-2c$ for many classes of graphs, where $ c $ is the number of odd cycles.