## Abstract

Topological descriptors are numerical parameters of a molecular graph which characterize its molecular topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. The counting polynomials are those polynomials having at exponent the extent of a property partition and coefficients the multiplicity/occurrence of the corresponding partition. All of the studied interconnection mesh networks in this paper are motivated by the molecular structure of a Sodium chloride NaCl. In this paper, Omega, Sadhana and PI polynomials are computed for mesh-derived networks. These polynomials were proposed on the ground of quasi-orthogonal cut edge strips in polycyclic graphs. These polynomials count equidistant and non-equidistant edges in graphs. Moreover, the analytical closed formulas of these polynomials for mesh-derived networks are computed for the first time.

Original language | English |
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Article number | 1850077 |

Journal | Discrete Mathematics, Algorithms and Applications |

Volume | 10 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 1 2018 |

## Keywords

- Counting polynomial
- Omega polynomial
- PI polynomial
- Sadhana polynomial
- mesh-derived network

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics