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Spectral radius and component factors in graphs

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Abstract

Let G be a graph and \(\mathcal {H}\) be a set of connected graphs. An \(\mathcal {H}\)-factor of G is a spanning subgraph, whose every component is isomorphic to a member of \(\mathcal {H}\). An \(\mathcal {H}\)-factor is also referred as a component factor. In this article, we present a spectral condition for a graph to admit a \(\{P_2,C_3, P_5,\mathcal {T}(3)\}\)-factor, where \(\mathcal {T}(3)\) is one special family of tree. Furthermore, we construct two extremal graphs to claim that the bounds on the spectral radius in our main result are sharp.

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Acknowledgements

The author is much grateful to the anonymous referees for their valuable comments on the paper, which have considerably improved the presentation of this paper. This work is supported by the Natural Science Foundation of Jiangsu Province (Grant No. BK20241949). Project ZR2023MA078 supported by Shandong Provincial Natural Science Foundation.

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  1. School of Science, Jiangsu University of Science and Technology, Zhenjiang, 212100, Jiangsu, China

    Sizhong Zhou

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  1. Sizhong Zhou
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S. Zhou wrote the main manuscript text.

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Zhou, S. Spectral radius and component factors in graphs. J Supercomput 81, 120 (2025). https://doi.org/10.1007/s11227-024-06522-x

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