A computational analysis of the face index of certain graph networks using multivariate regression

Abstract

Researchers have recently introduced a topological descriptor, called the face index, which quantifies the number of faces in a molecular network/compound to enhance efficiency by reducing computational time while improving the accuracy of chemical property calculations for chemical structures. It is observed that the face index provides valuable insights into the structural variations of different materials, offering a more generalized perspective compared to traditional vertex degree-based topological descriptors. This makes it a valuable tool for advancing research in chemistry and material science. Motivated by this, in the present study, we compute the face index for the chemical graphs of three significant networks namely the pentahexoctite, tetracyanobenzene and pyracyclene networks. Additionally, we perform a covariance analysis of this index with various degree-based topological indices for these networks. To further assess its predictability, we employ multivariate regression analysis, examining the relationship between the face index and these indices, which reveals a strong correlation between them.