Topological characterization for the line graph of nanostructures

A numerical quantity that characterizes the whole structure of a graph is called a topological index. More preciously topological indices are num-bers associated with molecular graphs for the purpose of allowing quantitative structure-activity/ property/ toxicity relationships. These topological indices correlate certain physico-chemical properties like boiling point, stability, strain energy etc of chemical compounds. The concepts of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index and Zagreb polynomials were established in chemical graph theory based on vertex degrees. These in-dices are useful in the study of anti-inflammatory activities of certain chemical networks. In this paper, we determine the hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index and Zagreb polynomials of the line graph of 2D-lattice, nanotube and nanotorus of TUC₄C₈[p, q] by using the concept of subdivision.