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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.02254 |
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| _version_ | 1866917380870897664 |
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| author | Wang, Shuai Cui, Lihong |
| author_facet | Wang, Shuai Cui, Lihong |
| contents | For a (molecular) graph $G$ and any real number $α\ne 0$ , the zero-order general Randić index , denote by $^0R_α$, is defined by the following equation: \begin{align*}
{^0R_α} (G) =\sum_{v\in G}d_G (v) ^α (α\in \mathbb{R}-\left\{0\right\}) . \end{align*}
In this paper, we use this index to give sufficient conditions for a graph $G$ to satisfy the Hamiltonian (or $k$-Hamiltonian) property, and show that none of these conditions can be dropped.
Finally we give similar results for the case when $G$ is a balanced bipartite graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02254 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sufficient conditions for Hamiltonianity in terms of the Zeroth-order General Randić Index Wang, Shuai Cui, Lihong Combinatorics For a (molecular) graph $G$ and any real number $α\ne 0$ , the zero-order general Randić index , denote by $^0R_α$, is defined by the following equation: \begin{align*} {^0R_α} (G) =\sum_{v\in G}d_G (v) ^α (α\in \mathbb{R}-\left\{0\right\}) . \end{align*} In this paper, we use this index to give sufficient conditions for a graph $G$ to satisfy the Hamiltonian (or $k$-Hamiltonian) property, and show that none of these conditions can be dropped. Finally we give similar results for the case when $G$ is a balanced bipartite graph. |
| title | Sufficient conditions for Hamiltonianity in terms of the Zeroth-order General Randić Index |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.02254 |