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Characterizations of Optimal Component Cuts of Locally Twisted Cubes

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Abstract

The k-component connectivity \(c\kappa _{k}(G)\) of a non-complete graph G is the minimum number of nodes whose deletion results in a graph with at least k components. A node subset S of G is called an optimal k-component cut if \(|S|=c\kappa _{k}(G)\) and \(G-S\) has exactly k components. In this paper, we determine the component connectivity of the locally twisted cube \(LTQ_{n}\), i.e. \(c\kappa _{k+1}(LTQ_{n})=kn-k(k+1)/2+1\) for \(1\le k\le n-1\), \(n\ge 2\), and characterize optimal k-component cuts of \(LTQ_{n}\).

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China

    Hui Shang, Eminjan Sabir & Jixiang Meng

  2. School of Applied Mathematics, Xiamen University of Technology, Fujian, 361024, China

    Litao Guo

Authors
  1. Hui Shang
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  2. Eminjan Sabir
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  3. Jixiang Meng
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  4. Litao Guo
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Correspondence to Jixiang Meng.

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Communicated by Rosihan M. Ali.

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The research is supported by NSFC (Nos. 11531011, 11301440).

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Shang, H., Sabir, E., Meng, J. et al. Characterizations of Optimal Component Cuts of Locally Twisted Cubes. Bull. Malays. Math. Sci. Soc. 43, 2087–2103 (2020). https://doi.org/10.1007/s40840-019-00792-y

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  • DOI: https://doi.org/10.1007/s40840-019-00792-y

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