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On the Number of Vertices with Specified Eccentricity

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Abstract.

The eccentricity of a vertex v in a graph is the maximum of the distances from v to all other vertices. The diameter of a graph is the maximum of the eccentricities of its vertices. Fix the parameters n, d, c. Over all graphs with order n and diameter d, we determine the maximum (within 1) and the minimum of the number of vertices with eccentricity c.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA. e-mail: mubayi@math.gatech.edu, , , , , , US

    Dhruv Mubayi

  2. Department of Mathematics, University of Illinois, Urbana, IL 61801, USA e-mail: west@math.uiuc.edu, , , , , , US

    Douglas B. West

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  1. Dhruv Mubayi
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  2. Douglas B. West
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Revised: May 7, 1999

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Mubayi, D., West, D. On the Number of Vertices with Specified Eccentricity. Graphs Comb 16, 441–452 (2000). https://doi.org/10.1007/PL00007229

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  • DOI: https://doi.org/10.1007/PL00007229

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