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The Sum Degree Distance and the Product Degree Distance of Generalized Transformation Graphs Gab

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Abstract:

In this contribution, we consider line splitting graph LS(G) of a graph G as transformation graph G++ of Gab. We investigate the sum degree distance DD+(G) and product degree distance DD*(G) of transformation graph Gab, which are weighted version of Wiener index. The Transformation graphs of Gab are G++, G+-, G-+ and G--.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 16)
Pages:
76-88
DOI:
https://doi.org/10.18052/www.scipress.com/BMSA.16.76
Citation:
K. G. Mirajkar and Y.B. Priyanka, "The Sum Degree Distance and the Product Degree Distance of Generalized Transformation Graphs Gab", Bulletin of Mathematical Sciences and Applications, Vol. 16, pp. 76-88, 2016
Online since:
Aug 2016
Authors:
Keerthi G. Mirajkar, Y.B. Priyanka
Keywords:
Degree Distance, Line Splitting Graph, Transformation Graph Gab
Export:
RIS, BibTeX, Text
Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

[1] G. Caporossi, M. Paiva, D. Vukičević, M. Segatto, Centrality and betweenness: vertex and edge decomposition of the Wiener index, MATCH Commun. Math. Comput. Chem., 68 (2012) 293–302.

[2] M.V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova, Huntington, NY, (2001).

[3] A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: theory and applications. Acta Appl Math, 66 (2001) 211-249.

[4] A.A. Dobrynin, A.A. Kochetova, Degree distance of a graph: a degree analogue of the Wiener index, J. Chem. Inf. Comput. Sci., 34 (1994) 1082–1086.

DOI: https://doi.org/10.1021/ci00021a008

[5] R.C. Entringer, D.E. Jackson, D. A. Snyder, Distance in graphs. Czechoslov Math. J., 26 (1976) 283–296.

[6] L. Feng, B. Liu, The maximal Gutman index of bicyclic graphs, MATCH Commun. Math. Comput. Chem., 66 (2011) 699–708.

[7] I. Gutman, Selected properties of the Schultz molecular topological index, J. Chem. Inf. Comput. Sci., 34 (1994) 1087–1089.

[8] F. Harary, Graph Theory, Addison-Wesley, Reading, (1969).

[9] A. Ili, D. Stevanovi, L. Feng, G. Yu, P. Dankelmann, Degree distance of unicyclic and bicyclic graphs, Discrete Appl. Math., 159 (2011) 779–788.

DOI: https://doi.org/10.1016/j.dam.2011.01.013

[10] D.J. Kelein , Z. Mihali, D. Plavši, N. Trinajsti, Molecular topological index: a relation with the Wiener index, J. Chem. Inf. Comput. Sci., 32 (1992) 304–305.

[11] V. R. Kulli, M. S. Biradar, The line splitting graph of a graph, Acta Ciencia Indica., XXVII, M. No. 3 (2002) 317–322.

[12] I. Tomescu, Ordering connected graphs having small degree distance, Discrete Appl. Math., 158 (2010) 1714–1717.

DOI: https://doi.org/10.1016/j.dam.2010.05.023

[13] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc., 69 (1947) 17-20.

[14] H. Wiener, Correlation of heats of isomerization and differences in heats of vaporization of isomers among the paraffin hydrocarbons, J. Am. Chem. Soc., 69 (1947) 2636–2638.

DOI: https://doi.org/10.1021/ja01203a022

[15] H. Wiener, Influence of interatomic forces on paraffin properties, J. Chem. Phys., 15 (1947) 766–766.

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