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The wide-diameter of regular graphs

  • School of Mathematical Sciences, University of Science and Technology of China；Wu Wentsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei 230026, China

Cite this: JUSTC, 2013, 43(8): 603-606
https://doi.org/10.3969/j.issn.0253-2778.2013.08.001
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  • Author Bio:

    LI Jiaao, male, born in 1990, master. Research field: Combinatorics and graph theory. E-mail: lijiaao@mail.ustc.edu.cn

  • Corresponding author:

    XU Junming

  • Received Date: December 19, 2012
  • Revised Date: May 21, 2013
  • Published Date: August 30, 2013
    Abstract
  • The diameter with width m of a graph G is defined as the minimum integer d for which between any two distinct vertices in G there exist at least m internally disjoint paths of length of at most d. It was shown that the tight upper bound on m-diameter of w-regular w-connected graph with order n is(n-2)(w-2)[](w-m+1)(3m-w-4)+1 for any integer m with 2w+5[]3≤m≤w. Some known results can be deduced or improved from the obtained result.
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