  A numerical parameter, known as a topological index, is employed to represent
the molecular structure of a compound by considering its graph-theoretical
properties. In the study of quantitative structure-activity relationships
(QSAR) and quantitative structure-property relationships (QSPR), topological
indices are used to predict the physicochemical properties of chemical
compounds. Graph entropies have evolved as information-theoretic tools to
investigate the structural information of a molecular graph. In this research
work, we compute the Nirmala index, the first and second inverse Nirmala index
for terpyridine complex nanosheet $TCN_{n,m}$ with the help of its
M-polynomial. Further, entropy measures based on Nirmala indices are calculated
for terpyridine complex nanosheets. We expand this analysis to include visual
comparisons, which could be useful in refining the structure for more effective
implementation. Furthermore, using graphical and numerical methods, the
correlation and comparison between the Nirmala indices and the corresponding
entropy measurements are shown. The relationship between the Nirmala indices
and associated entropy measurements is then examined using a regression model.
