Metric Dimension Of Different Chemical Structures

Abstract

In a simple way, we can define metric dimension of a graph G as, “It is the cardinality of resolving set.” Consider a connected graph G, in which V represents the vertex set and F represents the edge set and length of the shortest path between vertex p and qg is known as distance and can be denoted as d(p, q) in graph G. Consider an ordered set of vertices of graph G is L = fli, bh, ..., i} . The representation r(p|L) of with respect to L is the k — tuple (d(p, 11), d(p, 12), d(p, 13), ..., a(p, ld}, if distance of every single vertex of graph G from the vertices of L is different or we can say if two different vertices of graph G have different representations with respect to L then set L is said to be a resolving set. A resolving set having least number of vertices is said to be a basis set for graph G and this cardinality is known as the metric dimension of graph G and can be denoted as dim(G). Here, in this thesis we investigated metric dimension of Bakelite network