M-Polynomial and Related Topological Indices of Nanostar Dendrimers

Abstract

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.

M-Polynomial and Degree-Based Topological Indices of Polyhex Nanotubes

“…Recently, Munir et al computed M-polynomials and related topological indices for Nanostar dendrimers [15], titania nanotubes [16], and circulant graphs [17]. The structures of Nanostar dendrimers and titania nanotubes are different from polyhex nanotubes from a geometrical point of view.…”

“…Basic structural units of titania nanotubes are rectangles arranged differently for different types [16], whereas basic units of polyhex nanotubes are hexagons concatenated in different ways for different types. Nanostar dendrimers are macromolecules built on a tree-like structure [15]. Polyhex nanotubes have many applications in electronics, chemical processing, optics, and energy management [18,19] and are used in flat panel display screens [20], hydrogen storage, robotics and artificial muscles, chemical sensors, and photography.…”

Some Invariants of Jahangir Graphs

“…Hosoya polynomial [6] is one such well-known example which determines distance-based topological indices. M-polynomial [7], introduced in 2015, plays the same role in determining closed forms of many degree-based topological indices [8][9][10][11]. The main advantage of M-polynomial is the wealth of information that it contains about degree-based graph invariants.…”

Some Invariants of Circulant Graphs

“…Active research is in progress, and many authors computed M-polynomials for different types of nonmaterial, for example see [12][13][14][15][16] and the references therein.…”