Zagreb Connection Numbers of Different Chemical Graphs

Abstract

Topological indices are real numerical parameters of a molecular structural networks and structural networks. These networks are characterize its topology and graph invariant. The molecular networks plays a vital role in QSAR/QSPR study, phisco-chemical properties and topological indices like Randic, atom-bond connectivity(ABC) and geometric-arithmetic(GA) are used to diagnose the bioactivity of chemical compounds. Actually these topological indices is designed by transforming a chemical structure into a numeric number. In the area of research, graph theory has been found to be very useful. In this thesis, we will compute the connection based topological indices the so-called first Zagreb connection index, second Zagreb connection index and first modified Zagreb connection index of Honeycomb Network, Linegraph of Honeycomb Network, Line graph of subdivision of Honeycomb Network Triangular Benezenoid Network,line graph of sub-division of Triangular Benezenoid Network and Hourglass system. This study will give us a very interesting and different results by using new topological index that is first Zagreb, second Zagreb, first modified Zagreb connection index.