Computation of edge metric dimension of barcycentric subdivision of Cayley graphs

Z S Mufti (1) , M F Nadeem (1) , Ali Ahmad (2) , Z Ahmad (3)

1 COMSATS University Islamabad
2 Jazan University
3 Khwaja Fareed University of Engineering and Information Technology

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) .

Mots clés: metric dimension; edge metric dimension; resolving set; Cayley graph; barcycentric subdivi-sion

Domaines: Mathématique discrète [cs.DM]

Z S Mufti, M F Nadeem, Ali Ahmad, Z Ahmad. Computation of edge metric dimension of barcycentric subdivision of Cayley graphs. 2018. ⟨hal-01902772⟩