METRIC DIMENSION OF COMPLETE BIPARTITE DIGRAPHS

• Main Author: Hendy
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/33943
• Institution: Institut Teknologi Bandung

Let D be a digraph and n is the order of D: Let W = fw1;w2; :::;wkg be an ordered subset of V (D) and v be a vertex of D: A representation of v with respect to W is a k-vector r(vjW) = (d(v;w1); d(v;w2); :::; d(v;wk)), where d(x; y) denotes the directed distance of x to y; that is the length of the shortest directed path from x to y in D: If all vertices have representations and if two distinct vertices of D have distinct representation then W is a resolving set of D: The minimum cardinality of resolving set in D is the directed dimension or the metric dimension dim(D) of D: In this thesis we provide a sucient conditions for 2-dimensional digraph and discuss metric dimension of complete bipartite digraphs.