The Schultz, Modified Schultz indices and their polynomials of the Jahangir graphs Jn,m for integer numbersn=3, m≥3
Keywords:
Topological Index, Schultz Index, Schultz polynomials, Jahangir graphs J3, m.Abstract
Let G be a connected graph. The vertex-set and edge-set of G denoted by V(G) and E(G) respectively. The distance between the vertices u and v, d(u,v), in a graph is the number of edges in a shortest path connecting them.
In this study, we compute the Schultz Sc(G)=½(du+dv)d(u,v), Modified Schultz Sc*(G)=½(du×dv)d(u,v) indices and their polynomials of the Jahangir graphs Jn,m for integer numbers n=3, m≥3.
References
B. West, Introduction to graph theory. Prentice Hall of India, 2003.
H.P. Schultz, Topological organic chemistry 1. Graph theory and topological indices of alkanes. J. Chem. Inf. Comput. Sci. vol. 29, pp. 227–228, 1989.
S. Klavžar, I. Gutman. A Comparison of the Schultz Molecular Topological Index with the Wiener Index. J. Chem. Inf. Comput. Sci. vol. 36, pp. 1001-1003, 1996.
J. Devillers, A. T. Balaban, Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam, 1999.
R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, WileyVCH, Weinheim, 2000.
M. Karelson, Molecular Descriptors in QSAR/QSPR, Wiley Interscience, New York, 2000.
A. Iranmanesh and Y. Alizadeh, Computing Wiener and Schultz indices of HAC5C7[p,q] Nanotubes by GAP program. Am. J. Applied Sci., vol. 5, pp. 1754, 2008.
M. Eliasi and B. Taeri, Schultz Polynomials of Composite Graphs, Appl. Anal. Discrete Math. vol. 2, pp. 285-296, 2008.
A. Iranmanesh and Y. Alizadeh, Computing Szeged and Schultz Indices of HAC5C7C9[p,q] Nanotubes By Gap Program, Digest. J. Nanomater. Bios. vol. 4, no. 1 , pp. 67-72, 2009.
Y. Alizadeh, A. Iranmanesh and S. Mirzaie, Computing Schultz Polynomial, Schultz Index of C60 Fullerene By Gap Program. Digest. J. Nanomater. Bios. vol. 4, no. 1, pp. 7-10, 2009.
A. Iranmanesh and Y. Alizadeh, Computing Hyper-Wiener and Schultz Indices of TUZC6[p;q] Nanotubes By Gap Program. Digest. J. Nanomater. Bios. vol. 4, no. 1, pp. 607-611, 2009.
O. Halakoo, O. Khormali and A. Mahmiani, Bounds For Schultz Index of Pentachains. Digest. J. Nanomater. Bios. vol. 4, no. 4, pp. 687-691, 2009.
A. Heydari. On The Modified Schultz Index of C4C8(S) Nanotubes And Nanororus. Digest. J. Nanomater. Bios. vol. 5, no. 1, pp. 51-56, 2010.
A. Hedyari, Wiener and Schultz indices of V-Naphtalenic Nanotori. Optoelectron. Adv. Mater. – Rapid Commun. vol. 5, no. 7, pp. 786 - 789 , 2011.
M.R. Farahani, M.P. Vlad. On the Schultz, Modified Schultz and Hosoya polynomials and Derived Indices of Capra-designed planar Benzenoid. Studia UBB Chemia. vol. 57, no. 4, pp. 55-63, 2012.
M.R. Farahani. On the Schultz and Modified Schultz Polynomials of Some Harary Graphs. Int. J. Applications of Discrete Mathematics. vol. 1, no. 1, pp. 1-8, 2013.
M.R. Farahani. Hosoya, Schultz, Modified Schultz Polynomials and Their Topological Indices of Benzene Molecules: First Members of Polycyclic Aromatic Hydrocarbons (PAHs). International Journal of Theoretical Chemistry. vol. 1, no. 2, pp. 09-16, 2013.
M.R. Farahani. On the Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and Wiener index of Circumcoronene series of Benzenoid, J. Applied Math. & Info. vol. 31, no. (5-6), pp. 595-608, 2013.
N.K. Raut. Schultz, Modified Schultz and Hosoya polynomials and their indices in 2,3-dimethyl hexane an isomer of octane. Int. J. Mathematics and Computer Research. vol. 2, no. 8, pp. 587-592, 2014.
K. Ali, E.T. Baskoro and I. Tomescu, On the Ramzey number of Paths and Jahangir graph J3,m. 3rd International Conference on 21st Century Mathematics 2007, GC University Lahoor Pakistan, March, 2007.
D.A. Mojdeh and A.N. Ghameshlou. Domination in Jahangir Graph J2,m. Int. J. Contemp. Math. Sciences, vol. 2, no. 24, pp. 1193-1199, 2007.
A. Lourdusamy. Covering Cover Pebbling Number for Jahangir Graph J2, m. Sciencia Acta Xaveriana. vol. 4, no. 2, pp. 59-64, 2012.
A. Lourdusamy, S. Samuel Jeyaseelan and T. Mathivanan. On Pebbling Jahangir Graph. Gen. Math. Notes, vol. 5, no. 2, pp. 42-49, 2011.
A. Lourdusamy and T. Mathivanan. The 2t-Pebbling Property on the Jahangir Graph J2;m. Gen. Math. Notes, vol. 28, no. 1, pp. 18-39, 2015.
A. Lourdusamy and T. Mathivanan. The t-pebbling number of Jahangir graph J3,m. Proyecciones Journal of Mathematics. vol. 34, no. 2, pp. 161-174, 2012.
A. Lourdusamy, S.Samuel Jeyaseelan and T. Mathivanan. The t-Pebbling Number of Jahangir Graph. International J.Math. Combin. vol. 1, pp. 92-95, 2012.
M. Ramachandran and N. Parvathi. The Medium Domination Number of a Jahangir Graph Jm,n. Indian Journal of Science and Technology, vol. 8, no. 5, pp. 400–406, 2015.
M.R. Farahani, Hosoya Polynomial and Wiener Index of Jahangir graphs J2,m. Pacific Journal of Applied Mathematics. vol. 7 no. 3, In press, 2015.
M.R. Farahani, The Wiener Index and Hosoya polynomial of a class of Jahangir graphs J3,m. Fundamental Journal of Mathematics and Mathematical Science. vol. 3, no. 1, pp. 91-96, 2015.
M.R. Farahani, Hosoya Polynomial of Jahangir graphs J4,m. Global Journal of Mathematics. vol. 3, no. 1, pp. 232-236, 2015.
Downloads
Published
Issue
Section
License
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.
