A Proposed Method by Using the Adjacency Matrix to Solve the Edges Deletion Problem of Complete Graphs

Authors

  • Anwar Nasif Jasim Department of Mathematics, Faculty of CS and Mathematics University of Kufa, Iraq

DOI:

https://doi.org/10.31642/JoKMC/2018/120101

Keywords:

Edges deletion problem, Maximum diameter, Complete graph, Adjacency matrix .

Abstract

Graph theory approaches can be used to investigate a network’s dependability and effectiveness, and the network’s connectivity can be used to assess its dependability. The efficiency of a network is measured by its diameter, which can be somewhat increased by removing some vertices or edges. In this work, the maximum diameter fn(tt) of the modified graph G with n (n≥4) vertices, which resulted from removing t edges from the complete graph Kn ,(n≥4) was determined using the adjacency matrix adj(Kn).

Downloads

Download data is not yet available.

References

[1] H.R. Hashim, F. Luca, H.B. Shelash and A.A. Shukur, “Generalized Lucas graphs,” Afrika Matematika: Springer, vol. 34, no.1,p10, 2023, https://doi.org/10.1007/s13370-023-01048-6. DOI: https://doi.org/10.1007/s13370-023-01048-6

[2] F. Werner,” Graph-theoretic problems and their new applications. Mathematics,” MDPI ,vol.8, no.3,p 445, 2020, https://doi.org/10.3390/books978-3-03928-799-4 . DOI: https://doi.org/10.3390/math8030445

[3] J. L Kalb and D. S Lee, “Network topology analysis”, Technical report, Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States), 2008.

[4] V. Mohammadi, A. M. Rahmani, A. Darwesh and A. Sahafi, “Fault tolerance in fog-based Social Internet of Things,” Knowledge-Based Systems, vol. 265,pp110-376, 2023, https://doi.org/10.1016/j.knosys.2023.110376. DOI: https://doi.org/10.1016/j.knosys.2023.110376

[5] Y. Zou, L. Yang, G. Jing, R. Zhang and Z. Xie, “A sur vey of fault tolerant consensus in wireless networks,” High-Confidence Compu., 2024, https://doi.org/10.1016/j.hcc.2024.100202. DOI: https://doi.org/10.1016/j.hcc.2024.100202

[6] M.F. Nadeem, M. Imran, S. Afzal, M. Hafiz and Azeem, “Fault tolerance designs of interconnection networks, Peer-to-peer networking and applications,” Springer, vol.16, no.2, pp1125-1134, 2023, https://doi.org/10.1007/s12083-023-01462-4 . DOI: https://doi.org/10.1007/s12083-023-01462-4

[7] A.M. Rappoport and I.I. Kurochkin, “The graph diameter of a distributed system with a given dominant set,” 9th International Conference” Distributed Computing and Grid Technologies in Sci and Edu”(GRID 2021) Dubna, Russia,5-9, 2021, https://doi.org/10.54546/MLIT.2021.63.14.001. DOI: https://doi.org/10.54546/MLIT.2021.63.14.001

[8] N. Graham and F. Harary,” Changing and unchanging the diameter of a hypercube,” Discrete Applied Mathematics, vol. 37, pp265-274, 1992, https://doi.org/10.1016/0166 218X(92)90137-Y. DOI: https://doi.org/10.1016/0166-218X(92)90137-Y

[9] A. Bouabdallah, C. Delorme, and S. Djelloul, “Edge deletion preserving the diameter of the hypercube,” Discrete Applied Math., vol. 63, no. 1, pp 91-95, 1995, https://doi.org/10.1016/0166-218X(95)00023-K. DOI: https://doi.org/10.1016/0166-218X(95)00023-K

[10] A.A. Schoone, H.L. Bodlaender and L.J. Van, “Diameter increase caused by edge deletion,” Journal of graph theory, vol.11, no.3 ,pp409-427, 1987, https://doi.org/10.1002/jgt.3190110315. DOI: https://doi.org/10.1002/jgt.3190110315

[11] A.A. Najim and J. Xu , “Edge addition and edge deletion of graphs,” J. Univ. Sci. Technol. China, vol.36, no.3, pp254-257, 2006.

[12] A.N. Jasim and A.A. Najim, “Edges deletion problem of hypercube graphs for some n,” Discrete Mathematics, Algorithms and Applications,2024,https://doi.org/10.1142/S1793830924500459. DOI: https://doi.org/10.1142/S1793830924500459

[13] A.N. Jasim and A.A. Najim, “Solving Edges Deletion Problem of Generalized Petersen Graphs,” Journal of Kufa for Mathematics and Computer, vol.11, no.1, pp 6-10, 2024, http://dx.doi.org/10.31642/JoKMC/2018/110102. DOI: https://doi.org/10.31642/JoKMC/2018/110102

[14] A.N. Jasim and A.A. Najim, “Solving Edges Deletion Problem of Complete Graphs,” Baghdad Science Journal, vol.21, no.12, pp 4073-4082, 2024 https://doi.org/10.21123/bsj.2024.10128. DOI: https://doi.org/10.21123/bsj.2024.10128

[15] E.J. Kim, M. Milanic , J. Monnot and C. Picouleau, “Complexity and algorithms for constant diameter augmentation problems,” Theoretical Computer Science, vol. 904, pp 15-26, 2022, https://doi.org/10.1016/j.tcs.2021.05.020. DOI: https://doi.org/10.1016/j.tcs.2021.05.020

[16] M. Ju, J. Wang and S. Chang, “Diameter variability of hypercubes,” Theoretical Computer Science, vol. 542, pp 63-70, 2014, https://doi.org/10.1016/j.tcs.2014.04.033. DOI: https://doi.org/10.1016/j.tcs.2014.04.033

[17] S. F Florkowski, “Spectral graph theory of the hypercube”, Ph.D. thesis, Monterey, California. Naval Postgraduate School, https://hdl.handle.net/10945/3852, 2008.

Downloads

Published

2026-01-05

How to Cite

Nasif Jasim, A. (2026). A Proposed Method by Using the Adjacency Matrix to Solve the Edges Deletion Problem of Complete Graphs. Journal of Kufa for Mathematics and Computer, 12(1), 1-5. https://doi.org/10.31642/JoKMC/2018/120101

Share