ON THE METRIC DIMENSION OF BARYCENTRIC SUBDIVISION OF CAYLEY GRAPHS Cay(Zn⊕Zm).

Let W = {w1;w2; … ;wk} be an ordered set of vertices of G and let v be a vertex of G. The representation r(v|W) of v with respect to W is the k-tuple (d(v,w1),d(v,w2), … ; d(v,wk)). W is called a resolving set or a locating set if every vertex of G is uniquely identified by its distances from the vertices of W, or equivalently, if distinct vertices of G have distinct representations with respect to W . A resolving set of minimum cardinality is called a metric basis for G and this cardinality is the metric dimension of G, denoted by dim(G). Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). In this paper, we study the metric dimension of barycentric subdivision of Cayley graphs Cay(Zn ⊕Zm). We prove that these subdivisions of Cayley graphs have constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of Cayley graphs Cay(Zn⊕Zm). [ABSTRACT FROM AUTHOR]