Original Research Article

Article volume = 2023 and issue = 1

Pages: 75–84

Article publication Date: April 3, 2023

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# An Algorithmic Approach to Compute KCD Indices of Generalized Transformation Graphs G^{yz} and their Complements

#### Keerthi G. Mirajkar and Anuradha V. Deshpande

Department of Mathematics, Karnatak Universitys Karnatak Arts College, Dharwad - 580001, Karnataka, India.

##### Abstract:

This article focuses on the study of KCD indices for generalized transformation graphs $G^{yz}$ and their complements. In this study, the expressions for KCD indices of $G^{yz}$ and $\overline{G^{yz}}$ are obtained. Further the results are verified by an algorithmic approach.

##### Keywords:

KCD indices, Generalized transformation graphs, Algorithm.

##### References:

- [1] B. Basavanagoud, I. Gutman, and V. R. Desai, Zagreb indices of generalized transformation graphs and their complements, Kragujevac J. Sci., 37 (2015), 99–112. 2
- [2] I. Gutman, Degree based topological indices, Creat Chem. Acts, 86(4) (2013), 351–361. 1
- [3] I. Gutman and N. Trinajstic, Graph theory and molecular orbitals, Total- π electron energy of Alternant hydrocarbons, Chem. Phys., Let., 17 (1972), 535–538. 1
- [4] F. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem., 53(4) (2015), 1184—1190. 1
- [5] F. Harary, Graph Theory, Addison-Wesley, Mass, Reading, 1969. 1
- [6] H. Hosoya, A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn., 44(9) (1971), 2332—2339. 1
- [7] J. Li and W. C. Shiu, The harmonic index of a graph, Rocky Mountain J. Math., 44 (2014), 1607–1620. 1
- [8] K. G. Mirajkar and A. Morajkar, KCD indices and coindices of graphs, Ratio Mathematica, 39 (2020), 165–186. 2
- [9] H. S. Ramane, R. B. Jummannvar and S. Sedghi, Some degree base topological indices of generalized transformation graphs and their complements, Int. J. Pure Appl. Math., 109(3) (2016), 493–508. 2
- [10] M. Randi´c, Characterization of molecular branching, J. Am. Chem. Soc., 97(23) (1975), 6609—6615. 1
- [11] G. H. Shirdel, H. Rezapour and A. M. Sayadi, The hyper-Zagreb index of graph operations, Iranian J. Math. Chem., 4(2) (2013), 213–220. 1
- [12] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc., 69(1) (1947), 17—20. 1
- [13] B. Wu and J. Meng, Basic properties of total transformation graphs, J. Math. Study, 34(2) (2001), 110–117. 2

##### Cite this article as:

- Keerthi G. Mirajkar and Anuradha V. Deshpande, An Algorithmic Approach to Compute KCD Indices of Generalized Transformation Graphs G^{yz} and their Complements, Communications in Combinatorics, Cryptography & Computer Science, 2023(1), PP.75–84, 2023
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