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Minimum degree, edge-connectivity and radius

Author

Listed:
  • Baoyindureng Wu

    (Xinjiang University)

  • Xinhui An

    (Xinjiang University)

  • Guojie Liu

    (Xinjiang University)

  • Guiying Yan

    (Chinese Academy of Sciences)

  • Xiaoping Liu

    (Xinjiang Polytechnical College)

Abstract

Let G be a connected graph on n≥4 vertices with minimum degree δ and radius r. Then $\delta r\leq4\lfloor\frac{n}{2}\rfloor-4$ , with equality if and only if one of the following holds: (1) G is K 5, (2) G≅K n ∖M, where M is a perfect matching, if n is even, (3) δ=n−3 and Δ≤n−2, if n is odd. This solves a conjecture on the product of the edge-connectivity and radius of a graph, which was posed by Sedlar, Vukičević, Aouchice, and Hansen.

Suggested Citation

  • Baoyindureng Wu & Xinhui An & Guojie Liu & Guiying Yan & Xiaoping Liu, 2013. "Minimum degree, edge-connectivity and radius," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 585-591, October.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:3:d:10.1007_s10878-012-9479-6
    DOI: 10.1007/s10878-012-9479-6
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    References listed on IDEAS

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    1. Hansen, Pierre & Mladenovic, Nenad & Moreno Pérez, Jos´e A., 2008. "Variable neighborhood search," European Journal of Operational Research, Elsevier, vol. 191(3), pages 593-595, December.
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    Cited by:

    1. Kexiang Xu & Haiqiong Liu & Kinkar Ch. Das & Sandi Klavžar, 2018. "Embeddings into almost self-centered graphs of given radius," Journal of Combinatorial Optimization, Springer, vol. 36(4), pages 1388-1410, November.
    2. Kinkar Ch. Das & M. J. Nadjafi-Arani, 2017. "On maximum Wiener index of trees and graphs with given radius," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 574-587, August.
    3. Leanne Roncolato & John Willoughby, 2017. "Job Quality Complexities," Review of Radical Political Economics, Union for Radical Political Economics, vol. 49(1), pages 30-53, March.
    4. Siva Venkadesh & Anthony Santarelli & Tyler Boesen & Hong-Wei Dong & Giorgio A. Ascoli, 2023. "Combinatorial quantification of distinct neural projections from retrograde tracing," Nature Communications, Nature, vol. 14(1), pages 1-10, December.

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