Abstract:
The Metric Dimension of a graph G is the minimum number of basis element in a resolving
set. Let G = (V, E) be a connected graph and length of a shortest path between u and v is
known as distance, denoted by d(u, v) in G.
Let B = b1, b2, ..., bk be an ordered set of vertices of G. The representation r(u|B) of u
with respect to B is the k tuple (d(u, b1), d(u, b2), d(u, b3), ..., d(u, bk), where B is called a
resolving set or locating set if every vertex of G is uniquely identified by its distances from
the vertices of B or equivalently if distinct vertices of G have distinct representations with
respect to B. A resolving set of minimum cardinality is called a basis for G and cardinality
is the metric dimension of G is denoted by dim(G).
We investigated metric dimension on Line Graph of Polythiophene Network, Backbone
Network, Hex-derive Network and Chain Sillicate Network.
