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The spectral radius and domination number in linear uniform hypergraphs

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Abstract

This paper investigates the spectral radius and signless Laplacian spectral radius of linear uniform hypergraphs. A dominating set in a hypergraph H is a subset D of vertices if for every vertex v not in D there exists \(u\in D\) such that u and v are contained in a hyperedge of H. The minimum cardinality of a dominating set of H is called the domination number of H. We present lower bounds on the spectral radius and signless Laplacian spectral radius of a linear uniform hypergraph in terms of its domination number.

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Acknowledgements

Research was supported in part by the National Nature Science Foundation of China (Grant Nos. 11871329, 11571222).

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Liying Kang

  2. Centre of Excellence in Modelling and Simulation for Next Generation Ports, National University of Singapore, Singapore, Singapore

    Wei Zhang

  3. School of Management, Shanghai University, Shanghai, 200444, People’s Republic of China

    Erfang Shan

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  1. Liying Kang
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  2. Wei Zhang
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  3. Erfang Shan
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Correspondence to Erfang Shan.

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Kang, L., Zhang, W. & Shan, E. The spectral radius and domination number in linear uniform hypergraphs. J Comb Optim 42, 581–592 (2021). https://doi.org/10.1007/s10878-019-00424-y

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  • DOI: https://doi.org/10.1007/s10878-019-00424-y

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