Abstract
The relationship between Randić index, sum-connectivity index, harmonic index and \(\pi \)-electron energy of some benzenoid hydrocarbons is obtained.
Abbreviations
- n :
-
Number of observations of X and Y
- X[n]:
-
Array containing n values of predictor variable
- Y[n]:
-
Array containing n values of response variable
- SX :
-
Sum of all values of predictor
- SY :
-
Sum of all values of response
- \(SX^2\) :
-
Sum of squared X’s
- \(SY^2\) :
-
Sum of squared Y’s
- SXY :
-
Sum of product of X’s and Y’s
- \({\overline{X}}\) :
-
Mean of X’s
- \({\overline{Y}}\) :
-
Mean of Y’s
- SSXX :
-
Sum of squares for each X observation
- SSXY :
-
Sum of squares due to the pair X and Y
- \(c_0\) and \(c_1\) :
-
Regression coefficients
- R :
-
Correlation coefficient
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Acknowledgements
We are thankful to the anonymous referees for their helpful suggestions and bringing our attention to Ref. [12].
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This work was supported by the University Grants Commission (UGC), Govt. of India, through research grant under UPE FAR-II Grant No. F 14-3/2012 (NS/PE).
Second author V. B. Joshi died on 18 January 2018.
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Ramane, H.S., Joshi, V.B., Jummannaver, R.B. et al. Relationship Between Randić Index, Sum-Connectivity Index, Harmonic Index and \(\pi \)-Electron Energy for Benzenoid Hydrocarbons. Natl. Acad. Sci. Lett. 42, 519–524 (2019). https://doi.org/10.1007/s40009-019-0782-y
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DOI: https://doi.org/10.1007/s40009-019-0782-y
Keywords
- Benzenoid hydrocarbons
- Randić index
- Sum-connectivity index
- Harmonic index
- \(\pi \)-Electron energy
- Correlation
- Regression