Zagreb Indices and Coindices of Total Graph, Semi-Total Point Graph and Semi-Total Line Graph of Subdivision Graphs

Document Type: Original Scientific Paper

Authors

1 Department of Mathematics, Karnatak University, Dharwad, India

2 Faculty of Science, University of Kragujevac, Kragujevac, Serbia

Abstract

Expressions for the Zagreb indices and coindices of the total graph, semi-total point graph and of semi-total line graph of subdivision graphs in terms of the parameters of the parent graph are obtained, thus generalizing earlier existing results.

Keywords


[1] A. R. Ashrafi, T. Došlic and A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010) 1571–1578.
[2] B. Borovicanin, K. C. Das, B. Furtula and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem. 78 (2017) 17–100.
[3] J. Devillers and A. T. Balaban, Topological Indices and Related Descriptors in QSAR and QSPR, Gordon & Breach Science, Amsterdam, 1999.
[4] T. Došlic, Vertex–weighted Wiener polynomials for composite graphs, Ars Math. Comtemp. 1 (2008) 66–80.
[5] I. Gutman, Degree–based topological indices, Croat. Chem. Acta 86 (2013) 351–361.
[6] I. Gutman, B. Furtula, Ž. Kovijanic Vukicevic and G. Popivoda, On Zagreb indices and coindices, MATCH Commun. Math. Comput. Chem. 74 (2015) 5–16.
[7] F. Harary, Graph Theory, Addison Wesley, Reading, 1969.
[8] G. Mohanappriya and D. Vijayalakshmi, Topological indices of total graph of subdivision graphs, Ann. Pure Appl. Math. 14 (2017) 231–235.

[9] H. S. Ramane, V. V. Manjalapur and I. Gutman, General sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of line graph of subdivision graphs, AKCE Int. J. Graphs Comb. 14 (2017) 92–100.
[10] P. S. Ranjini, V. Lokesha and I. N. Cangül, On the Zagreb indices of the line graphs of the subdivision graphs, Appl. Math. Comput. 218 (2011) 699–702.
[11] E. Sampathkumar and S. B. Chikkodimath, Semi-total graphs of a graph, I, II, III, J. Karnatak Univ. Sci. 18 (1973) 274–280.
[12] R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics, Wiley–VCH Verlag GmbH & Co. KGaA, Weinheim, 2009.