ON THE TOTAL RESOLVING NUMBER OF WHEELS, FANS, TREES AND JAHANGIR GRAPH

• Main Author: Kekaleniate, Hikmatiarahmah
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/44464
• Institution: Institut Teknologi Bandung

Let G be a connected graph. Let S = fs1; s2; ; skg be a subset of V (G). For any v 2 (V (G)), the coordinate of v with respect to S is f(v) = (d(v; s1); d(v; s2); ; d(v; sk)). If distinct vertices in V have distinct coordinates, then S is called a resolving set of G. The cardinality of a minimum resolving set of G is called the metric dimension of G, (G). A resolving set S is called a total resolving set if the induced subgraph hSi has no isolated vertices. The cardinality of a total minimum resolving set of G is called the total resolving number of G and it is denoted by tr(G). In this project we give a study of tr(Wn), tr(fn), tr(Tn) and upper bound of tr(J2n), where Wn is a wheel on n + 1 vertices, fn is a fan on n + 1 vertices, Tn is a tree on n vertices, and J2n is a Jahangir graph on 2n + 1 vertices.