Novel Face Index for Benzenoid Hydrocarbons

Muhammad Kamran Jamil, Muhammad Imran and Kanza Abdul Sattar
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Muhammad Kamran Jamil: Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, 14 Ali Road, 54000 Lahore, Pakistan
Muhammad Imran: Department of Mathematical Sciences, College of Sciences, United Arab Emirates University, 15258 Al Ain, UAE
Kanza Abdul Sattar: Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, 14 Ali Road, 54000 Lahore, Pakistan

Mathematics, 2020, vol. 8, issue 3, 1-13

Abstract: A novel topological index, the face index ( F I ), is proposed in this paper. For a molecular graph G , face index is defined as F I ( G ) = ∑ f ∈ F ( G ) d ( f ) = ∑ v ∼ f , f ∈ F ( G ) d ( v ) , where d ( v ) is the degree of the vertex v . The index is very easy to calculate and improved the previously discussed correlation models for π - e l e c t r o n energy and boiling point of benzenoid hydrocarbons. The study shows that the multiple linear regression involving the novel topological index can predict the π -electron energy and boiling points of the benzenoid hydrocarbons with correlation coefficient r > 0.99 . Moreover, the face indices of some planar molecular structures such as 2-dimensional graphene, triangular benzenoid, circumcoronene series of benzenoid are also investigated. The results suggest that the proposed index with good correlation ability and structural selectivity promised to be a useful parameter in QSPR/QSAR.

Keywords: vertex degree; face degree; faces of a graph; face index; polycyclic aromatic hydrocarbons; ? -electron energy; boiling point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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