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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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| _version_ | 1866909670097027072 |
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| author | Samanta, Aniruddha |
| author_facet | Samanta, Aniruddha |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved bound of graph energy in terms of vertex cover number Samanta, Aniruddha Combinatorics Functional Analysis 05C22(primary), 05C50, 05C35(secondary) 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. |
| title | Improved bound of graph energy in terms of vertex cover number |
| topic | Combinatorics Functional Analysis 05C22(primary), 05C50, 05C35(secondary) |
| url | https://arxiv.org/abs/2507.00798 |