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Classes of Planar Graphs with Constant Edge Metric Dimension

Author

Listed:
  • Changcheng Wei
  • Muhammad Salman
  • Syed Shahzaib
  • Masood Ur Rehman
  • Juanyan Fang
  • M. Irfan Uddin

Abstract

The number of edges in a shortest walk (without repetition of vertices) from one vertex to another vertex of a connected graph G is known as the distance between them. For a vertex x and an edge e=ab in G, the minimum number from distances of x with a and b is said to be the distance between x and e. A vertex x is said to distinguish (resolves) two distinct edges e1 and e2 if the distance between x and e1 is different from the distance between x and e2. A set X of vertices in a connected graph G is an edge metric generator for G if every two edges of G are distinguished by some vertex in X. The number of vertices in such a smallest set X is known as the edge metric dimension of G. In this article, we solve the edge metric dimension problem for certain classes of planar graphs.

Suggested Citation

  • Changcheng Wei & Muhammad Salman & Syed Shahzaib & Masood Ur Rehman & Juanyan Fang & M. Irfan Uddin, 2021. "Classes of Planar Graphs with Constant Edge Metric Dimension," Complexity, Hindawi, vol. 2021, pages 1-10, April.
    • Handle: RePEc:hin:complx:5599274
    DOI: 10.1155/2021/5599274
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