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arXiv · 2604.02254

Sufficient conditions for Hamiltonianity in terms of the Zeroth-order General Randi\'c Index

Shuai Wang·Lihong Cui
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Abstract

For a (molecular) graph $G$ and any real number $\alpha\ne 0$ , the zero-order general Randi\'c index , denote by $^0R_\alpha$, is defined by the following equation: \begin{align*} {^0R_\alpha} (G) =\sum_{v\in G}d_G (v) ^{\alpha} (\alpha \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.

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Shuai Wang, Lihong Cui. 2026-04-02. Sufficient conditions for Hamiltonianity in terms of the Zeroth-order General Randi\'c Index. https://arxiv.org/abs/2604.02254

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