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文章基本信息

  • 标题:Resolvability in Subdivision of Circulant Networks Cn1,k
  • 本地全文:下载
  • 作者:Jianxin Wei ; Syed Ahtsham Ul Haq Bokhary ; Ghulam Abbas
  • 期刊名称:Discrete Dynamics in Nature and Society
  • 印刷版ISSN:1026-0226
  • 电子版ISSN:1607-887X
  • 出版年度:2020
  • 卷号:2020
  • 页码:1-11
  • DOI:10.1155/2020/4197678
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    Circulant networks form a very important and widely explored class of graphs due to their interesting and wide-range applications in networking, facility location problems, and their symmetric properties. A resolving set is a subset of vertices of a connected graph such that each vertex of the graph is determined uniquely by its distances to that set. A resolving set of the graph that has the minimum cardinality is called the basis of the graph, and the number of elements in the basis is called the metric dimension of the graph. In this paper, the metric dimension is computed for the graph G n 1 , k constructed from the circulant graph C n 1 , k by subdividing its edges. We have shown that, for k = 2 , G n 1 , k has an unbounded metric dimension, and for k = 3 and 4 , G n 1 , k has a bounded metric dimension.

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