SciELO - Scientific Electronic Library Online

vol.38 número5On star coloring of degree splitting of join graphs(p, q)-Lucas polynomials and their applications to bi-univalent functions índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados




Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.5 Antofagasta dic. 2019 


Computing the Schultz polynomials and indices for ladder related graphs

1Jazan University, College of Computer Sci. & Info. Technol., Jazan, Kingdom Saudi Arabia. E-mail:


Distance is an important graph invariant that has wide applications in computing science and other fields of sciences. A topological index is a genuine number connected with compound constitution indicating for relationship of compound structure with different physical properties, synthetic reactivity or natural action. The Schultz and modified Schultz polynomials and their corresponding indices are used in synthetic graph theory as in light of vertex degrees. In this paper, the Schultz and modified Schultz polynomials and their corresponding indices for Mongolian tent graph, diamond graph and double fan are determined.

Keywords: Distance; Topological indices; Schultz indices; Schultz polynomial

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


[1] A. Dobrynin, R. Entringer and I. Gutman, “Wiener index of trees: theory and applications”, Acta applicandae mathematicae, vol. 66, no. 3 pp. 211-249, May 2001, doi: 10.1023/A:1010767517079. [ Links ]

[2] M. Eliasi and B. Taeri, “Schultz polynomials of composite graphs”, Applicable analysis and discrete mathematics, vol. 2, no. 2, pp. 285-296, Apr. 2008. [On line]. Available: ]

[3] M. Farahani and M. Vlad, “On the Schultz, modified Schultz and Hosoya polynomials and derived indices of capradesigned planar benzenoid”, Studia universitatis Babeş-Bolyai, chemia, vol. 57, no. 4, pp. 55-63, 2012. [On line]. Available: ]

[4] M. 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. 9-16, Oct. 2013. [On line]. Available: ]

[5] M. Farahani , “On the Schultz and modified Schultz polynomials of some harary graphs”, International journal of applications of discrete mathematics, vol. 1, no. 1, pp. 1-8, Sep. 2013. [On line]. Available: ]

[6] M. Farahani , “On the Schultz polynomial and Hosoya polynomial of circumcoronene series of benzenoid”, Journal of applied mathematics & informatics, vol. 31, no. 5-6, pp. 595-608, 2013, doi: 10.14317/jami.2013.595. [ Links ]

[7] M. Farahani , “Schultz indices and Schultz polynomials of Harary graph”, Pacific journal of applied mathematics, vol. 6, no. 3, pp. 77-84, 2014. [ Links ]

[8] M. Farahani and W. Gao, “The Schultz index and Schultz polynomial of the Jahangir Graphs J5,m”, Applied mathematics, vol. 6, pp. 2319-2325, Dic. 2015, doi: 10.4236/am.2015.614204. [ Links ]

[9] M. Farahani , M. Kanna and W. Gao, “The Schultz, modified Schultz indices and their polynomials of the Jahangir graphs Jn,m for integer numbers n = 3, m ≥ 3”, Asian journal of applied sciences, vol. 3, no. 6, pp. 823-827, Dec. 2015. [On line]. Available: ]

[10] M. Farahani and M. Jamil, “The Schultz and modified Schultz polynomials of certain subdivision and line subdivision graphs”, Journal of chemical and pharmaceutical research, vol. 8, no. 3, pp. 51-57, 2016. [On line]. Available: ]

[11] I. Gutman, “Selected properties of the Schultz molecular topological index”, Journal of chemical information and modeling, vol. 34, no. 5, pp. 1087-1089, Sep. 1994, doi: 10.1021/ci00021a009. [ Links ]

[12] I. Gutman and O. Polansky, Mathematical concepts in organic chemistry, Berlin: Springer, 1986, doi: 10.1007/978-3-642-70982-1. [ Links ]

[13] F. Hassani, A. Iranmanesh and S. Mirzaie, “Schultz and modified Schultz polynomials of C100 Fullerene”, MATCH communications in mathematical and in computer chemistry, vol. 69, no. 1 pp. 87-92, 2013. [On line]. Available: ]

[14] H. Hosoya, “On some counting polynomials in chemistry”, Discrete applied mathematics, vol. 19, no. 1, pp. 239-257, Mar. 1988, doi: 10.1016/0166-218X(88)90017-0. [ Links ]

[15] S. Klavžar andI. Gutman , “Wiener number of vertex-weighted graphs and a chemical application”, Discrete applied mathematics , vol. 80, no. 1, pp. 73-81, Dec. 1997, doi: 10.1016/S0166-218X(97)00070-X. [ Links ]

[16] D. Klein, Z. Mihalić, D. Plavšić, N. Trinjastić, “Molecular topological index: a relation with the Wiener index”, Journal of chemical information and modeling , vol. 32, no. 4, pp. 304-305, Jul. 1992, doi: 10.1021/ci00008a008. [ Links ]

[17] M. Nadeem, S. Zafar and Z. Zahid, “On certain topological indices of the line graph of subdivision graphs”, Applied mathematicsand computation, vol. 271, pp. 790-794, Nov. 2015, doi: 10.1016/j.amc.2015.09.061. [ Links ]

[18] M. Nadeem , S. Zafar andZ. Zahid ,”On topological properties of the line graphs of subdivision graphs of certain nanostructures”, Applied mathematics and computation, vol. 273, pp. 125-130, Jan. 2016, doi: 10.1016/j.amc.2015.10.010. [ Links ]

[19] H. Schultz, “Topological organic chemistry 1. Graph theory and topological indices of alkanes”, Journal of chemical information and modeling, vol. 29, no. 3, pp. 227-228, Aug. 1989, doi: 10.1021/ci00063a012. [ Links ]

[20] M. Siddiqui, M. Imran and A. Ahmad, “On Zagreb indices, Zagreb polynomials of some nanostar dendrimers”, Applied mathematics and computation, vol. 280, pp. 132-139, Apr. 2016, doi: 10.1016/j.amc.2016.01.041. [ Links ]

[21] G. Su and L. Xu, “Topological indices of the line graph of subdivision graphs and their Schur-bounds”, Applied mathematics and computation, vol. 253, pp. 395-401, Feb. 2015, doi: 10.1016/j.amc.2014.10.053. [ Links ]

[22] H. Wiener, “Structural determination of the paraffin boiling points”, Journal of the American chemical society, vol. 69, no. 1, pp. 17-20, Jan. 1947, doi: 10.1021/ja01193a005. [ Links ]

Received: November 30, 2018; Accepted: January 30, 2019

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License