THE EDGE METRIC DIMENSION OF CAYLEY GRAPHS Γ(Z_n ⊕ Z_2) AND ITS BARYCENTRIC SUBDIVISIONS

Abstract

The main objective of this study is to determine the edge metric dimension(EMD) of the Cayley graphs Γ(Z_n ⊕ Z_2) and its barycentric subdivision. Infact, it is proved that the Cayley graphs and its subdivisions have constant EMD and its edge metric generator(EMG) set contains only three vertices to resolve all the edges of Cayley graphs Γ(Z_n ⊕ Z_2) and its barycentric subdivisions. In particular EMD remains invariant under the barycentric subdivisions of Γ(Z_n ⊕ Z_2). On the contrary, in [4] it was proved that the metric dimension of the Cayley graphs Γ(Z_n ⊕ Z_2) does not remain invariant under its barycentric subdivisions.