metric dimension of lexicographic product of some known‎ ‎graphs

For an ordered set w = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph g, the ordered k-vector r(v|w ) :=(d(v, w1), d(v, w2), . . . , d(v, wk)) is called the (metric) representation of v with respect to w , where d(x, y) is the distance between the vertices x and y. the set w is called a resolving set for g if distinct vertices of g have distinct representations with respect to w . the minimum cardi-nality of a resolving set for g is its metric dimension. in this paper, we investigate the metric dimension of the lexicographic product of graphs g and h, g[h], for some known graphs.