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Computation of edge metric dimension of barcycentric subdivision of Cayley graphs

Authors
  • Mufti, Z
  • Nadeem, M
  • Ahmad, Ali
  • Ahmad, Z
Publication Date
Oct 23, 2018
Source
HAL-UPMC
Keywords
Language
English
License
Unknown
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Abstract

Let G = (V, E) be a connected graph, let x ∈ V (G) be a vertex and e = yz ∈ E(G) be an edge. The distance between the vertex x and the edge e is given by d G (x, e) = min{d G (x, y), d G (x, z)}. A vertex t ∈ V (G) distinguishes two edges e, f ∈ E(G) if d G (t, e) = d G (t, f). A set R ⊆ V (G) is an edge metric generator for G if every two edges of G are distinguished by some vertex of R. The minimum cardinality of R is called the edge metric dimension and is denoted by edim(G). In this paper, we compute the edge metric dimension of barcycentric subdivision of Cayley graphs Cay(Z n ⊕ Z 2) .

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