A note on Adiga index for graphs
S Shashirekha, M Smitha, M P Ashwini, M S SurekhaBACKGROUND:
The term topological index is frequently reserved for graphical invariant molecular graph theory. Now, it is interconnected with machine learning. In the study of relationships using quantitative structure–property relationship (QSPR) and quantitative structure–activity relationship (QSAR), topological indices work as an important predictive tool for the physical and chemical properties of compounds. Their extended versions have become the most interesting part of the research because of their applications in the field of chemical sciences.
AIM:
In this research article, we introduce, Adiga index (AI) defined to be the sum of
METHODS:
The collected data were practically used to check the physical properties-boiling points (bp) C, molar volumes (mv) cm 3 , molar refractions (mr) cm 3 , heats of vaporization (hv) kJ, critical temperatures (ct) °C, critical pressures (cp) atm, and surface tensions (st) dyne cm − 1 , for lower alkanes and calculated AI and then analyses are being done to obtain regression models.
RESULTS:
Computations for Adiga index are carried out for some standard graphs and also for some chemical networks. Further, we compared AI with elliptic delta and modified elliptic delta index for oxide and hexagonal networks. We also relate the AI with the physical properties of lower alkanes using QSPR by obtaining an excellent, linear, regression model, which shows that AI may be employed as a predictive metric in the QSPR analysis.
CONCLUSION:
With the results we have obtained by introducing AI we are able to obtain excellent linear regression models in the form y = mx + b for physical properties of lower alkanes in terms of AI; it is shown that the AI may be employed as a predictive metric in QSPR analysis, for the physical properties of lower alkanes.