METRIC DIMENSION OF DIRECTED GRAPHS WITH CYCLIC COVERING - Pancahayani, Sigit
Let ????! G = (V;E) be a strongly connected directed simple graph with vertex set V and edge set E. For u; v 2 V ( ????! G ), the distance from u to v, d(u; v) is the minimum length of directed paths from u to v. Suppose B = fb1; b2; b3; :::bkg is a nonempty ordered subset of V . The representation of a vertex v with respect to B is dened as a vector (d(v; b1); d(v; b2); :::; d(v; bk)) and denoted by r(vjB). If any two distinct vertices u; v satisfy r(ujB) 6= r(vjB), then B is said to be a resolving set of G. If the cardinality of B is minimum, then B is said to be a basis of ????! G and the cardinality of B is called the metric dimension of ????! G which is denoted as dim( ????! G ). Let n 3 be a positive integer and ????! G admits a ????! Cn????covering. A simple???? ????! Cn orientation is an orientation on a directed graph ????! G such that every ????! Cn ????! G is strongly connected. This thesis deals with metric dimensions of directed friendship graphs ( ????! Fn), directed fan graphs ( ????????! Fm;n), directed wheel graphs ( ????! Wn), and amalgamation of directed cycle graphs.