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Journal of Information and Optimization Sciences

(Since 1980)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

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Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

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Journal of Information and Optimization Sciences
Open Access Research Article

Wiener index for a square of some special graphs

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pp. 1175–1185Vol. 47Issue 3March 2026DOI: 10.47974/JIOS-2156XML
Received:
01 Feb 2025
Published Online:
14 Mar 2026
Article type:
Research Article
Language:
EN
Article no.:
JIOS-2156
Pages:
1175–1185

Abstract

The importance of the operations defined in graph theory is determined by finding applications for them in other sciences, including chemistry, for example: If we have a simple connected graph whose edge set is non-empty and we want to define an operation in graph theory, such as a square operation, then the resulting new graph will be more realistic in chemistry, this is done by connecting edges between two vertices whose distance is one or two. In addition to the importance of finding the sum of thedistances betweenvertices, which represents the “Wiener’s index”, our interest in this research was to find the Wiener’s index for some special graphs after performing a squaring operation on it.

Keywords

Wiener indexSquare path graphSquare cycle graph

Subject Classifications

05C0905C3805C92

References

[1] G. Chartrand and L. Lesniak, Graphs and Digraphs, 6th ed. Pacific Grove, CA, USA,Wadsworth and Brooks/ Cole (2016).
[2] F. Buckley and F. Harary. Distance in Graphs, Addison – Wesley, Longman (1990).
[3] A. M. Ali, H. O. Abdullah and G. A. Mohammed Saleh, “Hosoya polynomials and Wiener indices of carbon nanotubes using mathematica programming”, Journal of Discrete Mathematical Sciences & Cryptography, vol. 25, no.1, pp. 147-158 (2022).
[4] H. Wiener, “Structural determination of paraffin boiling points,” J. Am. Chem. Soc., vol. 69, no. 1,pp. 17-20 (1947).
[5] M. Bojan and P. Tomaz, “How to Compute The Wiener Index of A Geaph”, Journal of Mathematical Chemistry, vol. 2, no.3, pp. 267 -277 (1988).
[6] N. Sonja and T. Nenad, “The Wiener Index: Development and Applications”, Croatica Chemica Acta, vol. 68, no.1, pp. 105-129 (1995).
[7] H. B. Walikar, V. S. Shigehalli and H. S. Ramane, “Bounds on the Wiener number of a graph”, Match Comm. Math. Comp. Chem. vol. 50, pp. 117–132, (2004).
[8] S. R. Harishchandra, S. R. Deepak and B. G. Asha, “ On The Wiener Index of A Graph”. J. Indones. Math. Soc., vol. 18, no.1, pp. 57–66 (2012).
[9] M. A. Ali, “ Some results on Wiener indices for a connected graph G”, Italian Journal of Pure Mathematics, no.46, pp. 391–399 (2021).
[10] G. Jayalalitha, M. Raji and S. Senthil, “ Hosoya Polynomial and Wiener Index of Molecular Graph of Naphthalene Based on Domination”, International Journal of Scientific Research and Review, vol. 8, no. 1, pp. 1238-1241 (2019).
[11] E. Mehdi E, R. Ghaffar, T. Bijan, “ Wiener index of some graph operations” , Discrete Applied Mathematics, vol.160, no. 9, pp. 1333-1344 (2012).
[12] H. N. Mohammed, H. D. Salim, and A. M. Ali, “Zagreb Indices for Chains of Identical Hexagonal cycles  Palestine”, Journal of Mathematics, vol. 12, no. 1, pp. 147–157 (2023).
[13] Q. S. Abdu and M. A, Y. A. Alameri, “ Topological Indices Types in Graph Theory and Their Applications”, Generis Publishing (2021).
[14] I. O. Zhian, O. A. Herish and M. A. Ahmed, “ D - index for a Chain of Hexagonal Cycles”. Palestine Journal of Mathematic, vol. 12, no. 1, pp.10–20 (2023).  
[15] M. A. Mahmood and M.A. Ahmed, “ Schultz and modified schultz polynomials for edge – Identification chain and ring  for –a square graphs”, Baghdad Science Journal, vol. 19, no. 3, pp. 560-568 (2022).
[16] H. Hongbo, “ Wiener and Schultz Molecular Topological Indices of Graphs with Specified Cut Edges”, Match Commun. Math. Comput. Chem, vol. 61, no. 3, pp. 643-651 (2009).
[17] A. M. Ali, and A. S. Aziz, “Relation between D-Index and Wiener Index for r-Regular Graphs” , International Journal of Mathematics and Mathematical, vol. 2020, pp. 1-6 (2020).
[18] C. S. Cambie and H. John, “On the relationship between variable Wiener index and variable Szeged index,” Applied Mathematics and Computation, vol. 431, pp. 1–8 (2022).
[19] K. C. Giovanna, K. G. Amir, J. M.  Harshit and N. Sergei; Parameterized algorithms for topological indices in chemistry. arXiv preprint arXiv preprint, pp. 1–19, (2023).  
[20] A. Meenakshi and M. Bramila, “Hosoya polynomial and Wiener index of Abid-Waheed graph (AW)a8 and (AW)a10,” Journal of Intelligent & Fuzzy Systems, pp. 1–8 (2024).
[21] E. O. Sozen, E. Eryasar, and C. Abdioglu, “Forgotten Topological and Wiener Indices of Prime Ideal Sum Graph of Zn”. Current Organic Synthesis, vol. 21, no. 3, pp. 239-245 (2024).
[22] G. Subashini, K. Kannan, and A. Menaga, “Exponential Wiener index of some silicate networks”. Scientific Reports, vol. 14, no. 1, pp. 27214. (2024).
[23] P. D. Khandare, S. M. Jogdand, and R. A. Muneshwar, “Energy and Wiener index of divisor graph of commutative ring,” Journal of Information and Optimization Sciences, vol. 44, no. 5, pp. 957–974 (2023).
[24] H. Al-Janabi, H. J. Mehdi, H. B. Ameen, and S. M. Kadham, “The Wiener index of some algebraic graphs and some applications,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 2, pp. 429–437 (2025).
[25] H. Hua and H. Liu, “Some results on vulnerability parameters and Wiener-type indices”, Discrete Applied Mathematics, vol. 358, pp. 262-271 (2024).
[26] F. Harary and I. C. Ross, “The square of a tree”,  Bell Syst. Tech. J., vol. 39, no. 3, pp. 641-647 (1960).

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