On The Metric Dimension of Some Operation Graphs

Abstract

Let be a simple, finite, and connected graph. An ordered set of vertices of a nontrivial connected graph is and the -vector represent vertex that respect to , where and is the distance between vertex and for . The set called a resolving set for if different vertex of have different representations that respect to . The minimum of cardinality of resolving set of G is the metric dimension of , denoted by . In this paper, we give the local metric dimension of some operation graphs such as joint graph , amalgamation of parachute, amalgamation of fan, and .

Keywords

• metric dimension, resolving set, operation graphs.