IJPAM: Volume 109, No. 3 (2016)

SOME DEGREE BASED TOPOLOGICAL INDICES
OF GENERALIZED TRANSFORMATION GRAPHS
AND OF THEIR COMPLEMENTS

Harishchandra S. Ramane$^1$, Raju B. Jummannaver$^2$, Shaban Sedghi$^3$
$^{1,2}$Department of Mathematics
Karnatak University
Dharwad, 580003, Karnataka, INDIA
$^3$Department of Mathematics
Qaemshahr Branch
Islamic Azad University
Qaemshahr, IRAN

Abstract. In this paper, the expressions for the Geometric-arithmetic index, Sum-connectivity index, Atom-bond connectivity index and Augmented Zagreb index of the generalized transformation graphs and of their complement graphs are obtained.

Received: March 13, 2016

Revised: May 27, 2016

Published: October 1, 2016

AMS Subject Classification: 05C76, 05C07, 92E10

Key Words and Phrases: geometric-arithmetic index, sum-connectivity index, atom-bond connectivity index, augmented Zagreb index, generalized transformation graphs
Download paper from here.

Bibliography

1
B. Basavanagoud, I. Gutman, V. R. Desai, Zagreb indices of generalized transformation graphs and their complements, Kragujevac J. Sci., 37 (2015), 99-112.

2
K. C. Das, On comparing Zagreb index of graphs, MATCH Commun. Math. Comput. Chem., 63 (2010), 433-440.

3
E. Estrada, Atom-bond connectivity and the energetic of branched alkanes, Chem. Phys. Lett., 463 (2008), 422-425.

4
E. Estrada, L. Torres, L. Rodríguez, I. Gutman, An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes, Indian J. Chem., 37A (1998), 849-855.

5
S. Fajtlowicz, On conjectures of Graffiti - II, Congr. Numer., 60 (1987), 187-197.

6
B. Furtula, A. Graovac, D. Vukicević, Augmented Zagreb index, J. Math. Chem., 48 (2010), 370-380.

7
I. Gutman, K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50 (2004), 83-92.

8
I. Gutman, N. Trinajstić, Graph theory and molecular orbitals, Total $\pi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17 (1972), 535-538.

9
X. Li, Y. Shi, A survey on the Randić index, MATCH Commun. Math. Comput. Chem., 59 (2008), 127-156.

10
J. Li, W. C. Shiu, The harmonic index of a graph, Rocky Mountain J. Math., 44 (2014), 1607-1620.

11
B. Lučić, S. Nikolić, N. Trinajstić, B. Zhou, S. Ivaniš Turk, Sum-connectivity index, in: I. Gutman, B. Furtula (Eds.), Novel Molecular Structure Descriptors - Theory and Applications I, Kragujevac Univ., Kragujevac, 2010, pp. 101-136.

12
B. Lučić, N. Trinajstić, B. Zhou, Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons, Chem. Phys. Lett., 475 (2009), 146-148.

13
H. S. Ramane, B. Basavanagoud, R. B. Jummannaver, Harmonic index and Randić index of generalized transformation graphs, preprint.

14
M. Randić, On characterization of molecular branching, J. Am. Chem. Soc., 97 (1975), 6609-6615.

15
E. Sampathkumar, S. B. Chikkodimath, Semitotal graphs of a graph - I, J. Karnatak Univ. Sci., 18 (1973), 274-280.

16
D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem., 46 (2009), 1369-1376.

17
B. Zhou, N. Trinajstić, On a novel connectivity index, J. Math. Chem., 46 (2009), 1252-1270.

.




DOI: 10.12732/ijpam.v109i3.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 3
Pages: 493 - 509


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).