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Minimum statuses of connected graphs with fixed maximum degree and order

Author

Listed:
  • Chiang Lin

    (National Central University)

  • Wei-Han Tsai

    (National Central University)

  • Jen-Ling Shang

    (Kainan University)

  • Yuan-Jen Zhang

    (National Central University)

Abstract

The status of a vertex in a connected graph is the sum of distances between the vertex and all vertices. The minimum status of a connected graph is the minimum of statuses of all vertices of this graph. In this paper we obtain the sharp lower bound and the sharp upper bound on the minimum status of a connected graph with maximum degree k and order n. All the graphs attaining the lower bound are obtained, and a necessary condition is given for those graphs attaining the upper bound.

Suggested Citation

  • Chiang Lin & Wei-Han Tsai & Jen-Ling Shang & Yuan-Jen Zhang, 2012. "Minimum statuses of connected graphs with fixed maximum degree and order," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 147-161, October.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9412-4
    DOI: 10.1007/s10878-011-9412-4
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    References listed on IDEAS

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    1. A. J. Goldman, 1972. "Minimax Location of a Facility in a Network," Transportation Science, INFORMS, vol. 6(4), pages 407-418, November.
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    Cited by:

    1. Lin, Hongying & Zhou, Bo, 2021. "Which numbers are status differences?," Applied Mathematics and Computation, Elsevier, vol. 399(C).

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