On M-polynomial-based topological descriptors of chemical crystal structures and their applications

A graph in which atoms are taken as vertices and bonds among atoms can be presented by edges is recognized as a molecular graph. For such molecular graphs, we can investigate the topological descriptors and topological polynomials providing their bioactivity as well as their physio-chemical characteristics. These topological descriptors are the numerical quantities of the molecular graph that discuss its topology and are usually graph invariants. Let m ab ( H ) where a , b ≥ 1 be the cardinality of edges uv in H such that ( Γ u , Γ v ) = ( a , b ) . M -polynomial for H can be computed by the relation M ( H ; z 1 , z 2 ) = ∑ a ≤ b m ab ( H ) z 1 a z 2 b . More preciously in this article, various molecular topological structure invariants of vital significance, known as first, second, modified and augmented Zagreb indices, inverse and general Randić indices, symmetric division, harmonic, inverse sum index and forgotten indices of chemical structures namely crystal cubic carbon CCC ( n ) and carbon graphite structure CG ( m , n ) are figured out and recovered applying general technique of topological polynomials.