Metric Dimension Of Different Chemical Structures

Abstract

Let G = (V,E) be a connected graph and distance between any two vertices m and n in G is (m−n) geodesic and is denoted by d(m,n). A set of vertices S resolves a graph G if each vertex is uniquely determined by its vector of distances to the vertices in S. A metric dimension of G is the minimum cardinality of a resolving set of G. In this thesis line graph of honeycomb network , azteic diamond,polycyclic aromatic hy drocarbon,triangualr benzenoid,honeycomb cup network has been derived and than calculate the metric dimension on line graph of Honeycomb network, azteic diamond ,polycyclic aromatic hydrocarbon, triangualr benzenoid and honeycomb cup network .