NONE 20260512111304075 wseas/wseas content-registration-form+ja@crossref.org content-registration-form WSEAS TRANSACTIONS ON MATHEMATICS 1109-2769 2224-2880 Eman Rawshdeh Department of Basic Scientific Sciences, Al-Huson University College, Al-Balqa Applied University, University, Irbid 21110, JORDAN Heba Adel Abdelkarim Department of Mathematics, Irbid National University, Irbid 21110, JORDAN Edris Rawashdeh Department of Mathematics, Yarmouk University, Irbid 21110, JORDAN 05 12 2026 05 12 2026 78 9 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/23206.2026.25.9 https://wseas.com/journals/mathematics/2026/a185106-2253.pdf H. Wiener. Structural determination of paraffin boiling points, J. Amer. Chem. Soc., Vol.69, 1947, pp. 17-20. A. A. Dobrynin, R. Entringer, and I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math., Vol.66, No.3, 2001, pp. 211- 249. A. A. Dobrynin, I. Gutman, S. Klavzar, P. Žigert, Wiener index of hexagonal systems, Acta Appl. Math. Vol. 72, No.3, 2002, pp. 247- 294. R.C. Entringer, Distance in graphs: Trees, J. Comb. Math. Comb. Comput., Vol.24, 1997, pp. 65-84. I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer Science & Business Media, 2012. I. Gutman, Y.-N. Yeh, S.-L. Lee, and Y.-L. Luo, Some recent results in the theory of the Wiener number, Indian J. Chem., Vol.32A, 1993, pp. 651-661. A. Alochukwu, P. Dankelmann, Wiener index in graphs with given minimum degree and maximum degree, Discrete Mathematics and Theoretical Computer Science, Vol.23, No.11, (2021). Y. N. Yeha, I. Gutmanb, On the sum of all distances in composite graphs, Discrete Math., Vol.135, 1994, pp.359-365. D. Stevanovi, Hosoya polynomial of composite graphs, Discrete Math., Vol.235, 2001, pp. 237-244. M. Eliasia, G. Raeisib, B. Taeri, Wiener index of some graph operations, Discrete Applied Mathematics, Vol.160, 2012, pp. 1333-1344. F. Belardo, M. Cavaleri, and A. Donno. Wreath product of a complete graph with a cyclic graph: topological indices and spectrum, Appl. Math. Comput., Vol.336, 2018, pp. 288- 300. M. Cavaleri and A. Donno, Some degree and distance-based invariants of wreath products of graphs, Discrete Appl. Math. Vol.277, 2020, pp. 22- 43 A. Donno. Spectrum, distance spectrum, and Wiener index of wreath products of complete graphs, Ars Math. Contemp., Vol.13, No.1, 2017, pp. 207- 225. R.L. Graham, H.O. Pollak, On the addressing problem for loop switching, Bell Syst. Tech. J., Vol. 50, 1971, pp. 2495-2519. N. Alon, Neighborly families of boxes and bipartite coverings, Algorithms and Combinatorics, Vol.14, 1997, pp. 27-31. E. Kushilevitz and N. Nisan, Communication Complexity Cambridge, 1996. D.S. Nau, G. Markowski, M. A. Woodbury and D. B. Amos, A Mathematical Analysis of Human Leukocyte Antigen Serology, Mathematical Biosciences, Vol.40, 1978, pp. 243- 270. E. Ghorbani, H. R. Maimani, On eigensharp and almost eigensharp graphs. Linear Algebra Its Appl, Vol.429, 2008, pp. 2746-2753. T. Kratzke, B. R. Reznick, D. West, Eigensharp graphs: Decomposition into complete bipartite subgraphs, Trans. Amer. Math. Soc. , 308, 637--653 (1988). T. Pinto, Biclique Covers and decompositions, Electron. J. Comb., Vol.21, 2014, pp. 1-19. E. Rawshdeh, H. Abdelkarim and E. Rawashdeh, On the Eigensharp of Corona Product, Int. J. Math. Comput. Sci., Vol.17, 2022, 865-874. N. Ashrafi, H. R. Maimani, M. R. Pournaki and S. Yassemi, Unit graphs associated with rings, Commun. Algebra, Vol.38, 2010, pp. 2851-2871. H. Abdelkarim, E. Rawshdeh, E. Rawashdeh, The Eigensharp Property for Unit Graphs Associated with Some Finite Rings, Axioms, Vol.11, No.7, 2022, pp. 349. 349 (2022). A. Saleh, A. Alqesmah, H. Alashwali and I.N. Cangul, Entire Wiener index of graphs, Communications in Combinatorics & Optimization, Vol.7, No.2, 2022, 1-19.