Abstract:
A topological index is a numerical value that characterizes the topology of a graph.
Topological indices of molecular graphs are crucial in Chemical Graph Theory and can
be utilized to examine the chemical properties of medications. Topological indices can
be utilized for predicting the physical properties of some dangerous drugs without
having costly and time-consuming laboratory experiments. In 1972, Gutman and
Trinajstić introduced the first and second Zagreb indices. Then the first and second
Zagreb polynomials were derived by Fath-Tabar in 2009. There are more than 3000
topological indices in the literature. The first objective of this study is to compute the
Contra-Harmonic index which was defined by S.Ragavi and R. Sridevi in 2020 for
some nanotubes and nanotorus, namely V-Phenyline Nanotube (VPHX[m,n]), V
Phenyline Nanotorus (VPHY(m.n)), H-Naphtalenic nanotubes (NHPX[m, n]). The
second objective of the study is to define the topological polynomial using the Contra
Harmonic index and compute the polynomials for the aforesaid nano structures. Here,
the hydrogen-suppressed chemical graphs of the nano compounds were considered to
treat atoms as vertices and chemical bonds as the edges of the chemical graphs. The
computed Contra-Harmonic indices and corresponding polynomials are expected to
offer valuable insights into the physicochemical properties of these compounds,
enhancing the understanding and applications of these nanostructures in drug design
and related fields.
