Classes of Planar Graphs with Constant Edge Metric Dimension

Changcheng Wei, Muhammad Salman, Syed Shahzaib, Masood Ur Rehman, Juanyan Fang and M. Irfan Uddin

Complexity, 2021, vol. 2021, 1-10

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:5599274

DOI: 10.1155/2021/5599274

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