Computation of edge metric dimension of barcycentric subdivision of Cayley graphs

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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Submitted on : Tuesday, October 23, 2018 - 5:59:15 PM
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Z Mufti, M Nadeem, Ali Ahmad, Z Ahmad. Computation of edge metric dimension of barcycentric subdivision of Cayley graphs. 2018. ⟨hal-01902772⟩

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