Abstract
During the last decade, several research groups have published results on sufficient conditions for the hamiltonicity of graphs by using some topological indices. We mainly study hyper-Zagreb index and some hamiltonian properties. We give some sufficient conditions for graphs to be traceable, hamiltonian or Hamilton-connected in terms of their hyper-Zagreb indices. In addition, we also use the hyper-Zagreb index of the complement of a graph to present a sufficient condition for it to be Hamilton-connected.
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The authors are grateful to the anonymous referees for the valuable comments, suggestions and corrections which improved the presentation of this paper.
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This work was supported by the National Natural Science Foundations of China (No. 11901253), the Natural Science Foundation for Colleges and Universities in Jiangsu Province of China (Nos. 19KJB110009, 21KJB110025), and the Science Foundation of Jiangsu Normal University (Nos. 18XLRX021, 20XFRS001).
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Lu, Y., Zhou, Q. On hyper-Zagreb index conditions for hamiltonicity of graphs. Czech Math J 72, 653–662 (2022). https://doi.org/10.21136/CMJ.2022.0089-21
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DOI: https://doi.org/10.21136/CMJ.2022.0089-21