Relationship Between Randić Index, Sum-Connectivity Index, Harmonic Index and \(\pi \)-Electron Energy for Benzenoid Hydrocarbons

Abstract

The relationship between Randić index, sum-connectivity index, harmonic index and \(\pi \)-electron energy of some benzenoid hydrocarbons is obtained.

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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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Correspondence to H. S. Ramane.

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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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Keywords

  • Benzenoid hydrocarbons
  • Randić index
  • Sum-connectivity index
  • Harmonic index
  • \(\pi \)-Electron energy
  • Correlation
  • Regression

Mathematics Subject Classification

  • 92E10
  • 05C07