Topological Indices on Line Graphs of Multi Wheel Graphs and Multi Prism Graphs

Abstract

Topological index is a numerical quantity which characterizes the whole structure of a graph. These indices are invariants under the graph isomorphism which characterizes its topology and are usually hold mathematical properties of graph invariant. Related to chemistry, actually it is a numerical quantity linked with chemical structure express for the relationship of chemical network with various physical-chemical characteristics like temperature, boiling points and path number etc. Actually these topological indices are formulated by transforming a chemical structure into a numeric number. In the area of research graph theory has been found to be very beneficial. In this thesis, we will calculate the degree based topological indices so-called Randic index, atom bond connectivity (ABC) index, geometric arithmetic(GA) index, first and second Zagreb, second modified Zagreb, third Zagreb, hyper Zagreb, Harmonic index, F-index, Shigehalli and Kanubar index for line graph of multi-wheel graph 𝑊𝑚 = (𝐶𝑛 × 𝑃𝑚) where 𝑚 ≥ 2 as well as line graph of multi-prism graph 𝑌𝑚,𝑛 = (𝐶𝑚 × 𝑃𝑛) where 𝑛 ≥ 4. We will also calculate degree sum based topological indices ABC₄ index known as the forth version of atom bond connectivity (ABC) index and GA₅ index which is the fifth class of geometric arithmetic (GA) index for these graphs. This study will give us a very interesting and different results by using new topological index that is first Zagreb and second Zagreb, second modified Zagreb, third Zagreb, hyper and augmented Zagreb topological indices.