TARU PUBLICATIONS
Journal of Information and Optimization Sciences cover

Journal of Information and Optimization Sciences

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

The Journal of Information and Optimization Sciences (JIOS) is a world leading journal publishing high quality, rigorously peer-reviewed original research in all mathematically-oriented theoretical and applied topics in information sciences, optimization sciences and related areas since 1980. Subjects include but are not limited to: • Information Sciences • Optimization Sciences • Control Theory • Operational Research • Decision Sciences • Information Theory • Information Technology • Computer Networks and Communications • Mathematical Programming • Modelling and Simulation • Database Management • Applications to Engineering Sciences • Applications to Technology

Issues up to 2022 co-published with and available at:Taylor & Francis
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Information and Optimization Sciences
Open Access Research Article

A useful encryption of discrete graphs on symmetric groups

* ,

* Corresponding author · click or hover a name for details

pp. 1–14Online FirstFebruary 2026DOI: 10.47974/JIOS-1941XML
Received:
16 Aug 2024
Published Online:
14 Feb 2026
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1941
Pages:
1–14

Abstract

In recent years, graph theory has become much more popular due to its wide range of applications in almost every field of interest. Especially, it plays an integral role in cryptography and coding theory to develop new security systems. In this article, we introduce and investigate novel discrete graphs arising from symmetric groups and incorporate these graphs to communicate confidential messages via an interesting encryption. These newly defined discrete graphs are termed as Order Incongruent Simple Graphs (OISG). The vertices of these graphs are the permutations of the symmetric groups, and edges are defined via modular arithmetic. Many fascinating structures and characterizations of these graphs are proposed and proved using congruences from number theory. 

Keywords

Symmetry groupsOrder incongruent graphModular arithmeticCryptography

Subject Classifications

05C2505C7505C50

References

[1] A. S. Alali, S. Ali, N. Hassan, A. M. Mahnashi, Y. Shang, and A. Assiry, Algebraic structure graphs over the commutative ring Zm: exploring topological indices and entropies using M-polynomials, Mathematics, vol. 11, no. 18, p. 3833, (2023).
[2] T. Domada, S. A. Kumar, G. Ashok, and D. C. Kumari, Super-encryption with Pell-Lucas matrices and graphs via Laplace transformations, J. Harbin Eng. Univ., vol. 44, no. 8, (2023).
[3] T. Domada, G. Ashok, S. A. Kumar, and D. C. Kumari, Super-encryption technique of graphs via matricial approach, J. Discrete Math. Sci. Cryptogr., vol. 27, no. 4, pp. 1215-1222, (2024).
[4] A. G. Syarifudin, D. P. Malik, and I. G. A. W. Wardhana, Some characterization of coprime graph of dihedral group D2n, in J. Phys.: Conf. Ser., vol. 1722, no. 1, p. 012051, (2021).
[5] J. Friedman, On Cayley graphs on the symmetric group generated by transpositions, Combinatorica, vol. 20, no. 4, pp. 505-519, (2000).
[6] L. Somer and M. Krek, On a connection of number theory with graph theory, Czechoslovak Math. J., vol. 54, pp. 465-485, (2004).
[7] D. Namli, Some results on cubic residues, Int. J. Algebra, vol. 9, pp. 245-249, (2015).
[8] M. H. Mateen, M. K. Mahmmod, D. Alghazzawi, and J. B. Liu, Structures of power digraphs over the congruence equation xp ≡ y(mod m) and enumerations, AIMS Math., vol. 6, no. 5, pp. 4581-4596, (2021).
[9] S. Asif, M. K. Mahmood, A. S. Alali, and A. A. Zaagan, Structures and applications of graphs arising from congruences over moduli, AIMS Math., vol. 9, no. 8, pp. 21786-21798, (2024).
[10] S. Asif and M. K. Mahmood, Structural properties of the graphs arising from congruences over set of moduli, JP J. Algebra Number Theory Appl., vol. 64, no. 1, pp. 81-98, (2025).
[11] S. Al-Kaseasbeh and A. Erfanian, A bipartite graph associated to elements and cosets of subgroups of a finite group, AIMS Math., vol. 6, no. 10, pp. 10395-10404, (2021).
[12] Aneela, M. K. Mahmood, and D. Ahmad, Order structured graphs of cyclic groups and their classification, VFAST Trans. Math., vol. 12, no. 1, pp. 220-233, (2024).
[13] M. U. Romdhini, A. Nawawi, and C. Y. Chen, Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups, Malays. J. Math. Sci., vol. 17, no. 1, pp. 53-65, (2023).

Views: 12Downloads: 8Citations: 0