Let G be a simple connected graph, the vertex- set and edge- set of G are denoted by V(G) and E(G), respectively. The molecular graph G, the vertices represent atoms and the edges represent bonds. In graph theory, we have many invariant polynomials and many invariant indices of a connected graph G. Topological indices based on the distance between the vertices of a connected graph are widely used in theoretical chemistry to establish relation between the structure and the properties of molecules. The coefficients of polynomials are also important in the knowledge some properties in application chemistry. The Schultz and modified Schultz polynomials, Schultz and modified Schultz indices and average distance of Schultz and modified Schultz of Cog-complete bipartite graphs are obtained in this paper.
| Published in | Applied and Computational Mathematics (Volume 6, Issue 6) |
| DOI | 10.11648/j.acm.20170606.14 |
| Page(s) | 259-264 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
Schultz and Modified Schultz Polynomials, Cog-Complete Bipartite Graphs, Topological Indices, Boundary Average Distance
| [1] | Wiener, H.; (1947), “Structural Determination of Paraffin Boil- ing Points” J. Amer. Chem. Soc., 69, 17-20. |
| [2] | Diudea, M. V. (ed.); (2001). QSPR/QSAR Studies by Molecular Descriptors, Nova, Huntington, New York. |
| [3] | Diudea, M. V., Gutman, I. and J¨antschi, L.; (2001). Molecular Topology, Nova, Huntington, New York. |
| [4] | Chartrand, G. and Lesniak, L.; (1986). Graphs and Digraphs, 2nd ed., Wadsworth and Brooks/Cole, California. |
| [5] | Devillers, J. and Balaban, A. T. (eds.); (1999). Topological Indices and Related Descriptors in QSAR and QSPR, Gordon & Breach, Amsterdam. |
| [6] | Diestel, R.; (2000). Graph Theory, electronic ed., Springer- Verlag, New York. |
| [7] | Farahaini M. R., (2013); "Hosoya, Schultz Modified Schultz Polynomials and their Topological Indices of Benzene Molecules: First Members of polycyclic Aromatic Hydro Carbons (PAHs)"; International Journal of theoretical chemistry Vol. 1, No. 2, pp. 6-9. |
| [8] | Farahaini M. R., On the Schultz Polynomial, Modified Schultz Polynomial, Hosoya polynomial and Wiener Index of Circumcoronene Series of Benzenoid. Journal of Applied Mathematics of infromatics, (2013), 31 (5-6). |
| [9] | Haoer, R. S., Atan, K. A., Khalaf, A. M., Rushdan, M. and Hasni, R (2016); Eccentric Connectivity Index of Some Chemical Trees, International Journal of Pure and Applied Mathematics, Vol. 106, No. 1, pp. 157-170. |
| [10] | Schultz, H. P. (1989), "Topological Organic Chemistry 1". Graph theory and topological indices of alkanes. J. Chem. Inf. Copmut. Sci. 29, 227-228. |
| [11] | Klavz ̆ar, S. and Gutman, I. (1997), "Wiener number of vertex –weighted graphs and a chemical application". Disc. Appl. Math. 80, 73-81. |
| [12] | Gutman, I. (2005), “Some Relations Between Distance- Based Polynomials of Trees”. Bull. A cod. Serbe. Sci. Arts 131, pp. 1-7. |
| [13] | Bo Zhou, (2006), “Bounds for the Schultz Molecular Topol- ogical Index” MATCH Commun. Math Comput. Chem. Vol. 56, pp. 189-194. |
| [14] | Behmaram, A, Yousefi- Azari, H. and Ashrafi, A. R., (2011); "Some New Results on Distance–Based Polynomials", MATH. Commun. Math. Comput. Chem. 65, 39-50. |
| [15] | Hassani, G., Iranmanesh, A. and Mirzaie, S. (2013), “Schultz and Modified Schultz Polynomials of C100 Fullerene”. MATCH Commun. Math. Comput. Chem. Vol. 69, pp. 87-92. |
| [16] | Iranmanesh, A. and Ali zadeh, Y., (2009), “Computing Szeged and Schultz Indices of HAC3C7C9[p,q] Nanotube by Gap program. Digest Biostructures, 4, pp. 67-72. |
| [17] | Heydar. A., (2010), “Schultz Index of Regular Dendrimers” optoelectronics and Advanced Materials: Rapid Communi-cations, 4, pp. 2209-2211. |
| [18] | Heydari, A., (2010),“On the Modified Schultz Index of C4C8(S) Nanotubes and Nanotours. Digest Journal of Nanomatrial and Biostructures, 5, pp. 51-56. |
| [19] | Farahaini M. R., (2014); "Schultz and Modified Schultz Polyn- omials of Coronene Polycyclic Aromatic Hydro carbons", International Letters of chemistry, Physics and Astronomy, Vol. 32, pp. 1-10. |
| [20] | Farahani M. R., (2013); "On the Schultz and Modified Schultz Polynomials of Some Harary Graphs", International Journal of Applications of Discrete Mathematics; Vol. 1, No. 1, pp. 01-08. |
| [21] | Guo. H. and Zhow B.; (2017), "Properties of Degree Distance and Gutman Index of Uniform Hypergraphs" MATCH Commun. Math. Comput Chem. 78, pp. 213-220. |
APA Style
Ahmed Mohammed Ali, Haitham Nashwan Mohammed. (2017). Schultz and Modified Schultz Polynomials of Cog-Complete Bipartite Graphs. Applied and Computational Mathematics, 6(6), 259-264. https://doi.org/10.11648/j.acm.20170606.14
ACS Style
Ahmed Mohammed Ali; Haitham Nashwan Mohammed. Schultz and Modified Schultz Polynomials of Cog-Complete Bipartite Graphs. Appl. Comput. Math. 2017, 6(6), 259-264. doi: 10.11648/j.acm.20170606.14
AMA Style
Ahmed Mohammed Ali, Haitham Nashwan Mohammed. Schultz and Modified Schultz Polynomials of Cog-Complete Bipartite Graphs. Appl Comput Math. 2017;6(6):259-264. doi: 10.11648/j.acm.20170606.14
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.acm.20170606.14,
author = {Ahmed Mohammed Ali and Haitham Nashwan Mohammed},
title = {Schultz and Modified Schultz Polynomials of Cog-Complete Bipartite Graphs},
journal = {Applied and Computational Mathematics},
volume = {6},
number = {6},
pages = {259-264},
doi = {10.11648/j.acm.20170606.14},
url = {https://doi.org/10.11648/j.acm.20170606.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170606.14},
abstract = {Let G be a simple connected graph, the vertex- set and edge- set of G are denoted by V(G) and E(G), respectively. The molecular graph G, the vertices represent atoms and the edges represent bonds. In graph theory, we have many invariant polynomials and many invariant indices of a connected graph G. Topological indices based on the distance between the vertices of a connected graph are widely used in theoretical chemistry to establish relation between the structure and the properties of molecules. The coefficients of polynomials are also important in the knowledge some properties in application chemistry. The Schultz and modified Schultz polynomials, Schultz and modified Schultz indices and average distance of Schultz and modified Schultz of Cog-complete bipartite graphs are obtained in this paper.},
year = {2017}
}
TY - JOUR T1 - Schultz and Modified Schultz Polynomials of Cog-Complete Bipartite Graphs AU - Ahmed Mohammed Ali AU - Haitham Nashwan Mohammed Y1 - 2017/12/18 PY - 2017 N1 - https://doi.org/10.11648/j.acm.20170606.14 DO - 10.11648/j.acm.20170606.14 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 259 EP - 264 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20170606.14 AB - Let G be a simple connected graph, the vertex- set and edge- set of G are denoted by V(G) and E(G), respectively. The molecular graph G, the vertices represent atoms and the edges represent bonds. In graph theory, we have many invariant polynomials and many invariant indices of a connected graph G. Topological indices based on the distance between the vertices of a connected graph are widely used in theoretical chemistry to establish relation between the structure and the properties of molecules. The coefficients of polynomials are also important in the knowledge some properties in application chemistry. The Schultz and modified Schultz polynomials, Schultz and modified Schultz indices and average distance of Schultz and modified Schultz of Cog-complete bipartite graphs are obtained in this paper. VL - 6 IS - 6 ER -
Email: