A bipartite graph associated to Hamiltonian degrees of finite groups
A. Erfanianerfanian@um.ac.irDepartment of Pure Mathematics Centre of Excellence in Analysis on Algebraic Structures Faculty of Mathematical Sciences Ferdowsi University of MashhadMashhad, 91775, IranView full profile → , S. Al-Kaseasbehsaba.alkaseasbeh@gmail.comDepartment of Mathematics Tafila Technical UniversityTafila, 66110, JordanView full profile → , *M. Al TahanCorresponding authoraltahan.madeleine@gmail.comDepartment of Mathematics and Statistics Abu Dhabi UniversityAbu Dhabi, 59911, United Arab EmiratesView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Jan 2025
- Published Online:
- 11 Mar 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2594
- Pages:
- 1421–1434
Abstract
Keywords
Subject Classifications
References
[1] S. Al-Kaseasbeh and J. Coykendall, “Adjacency-like conditions and induced ideal graphs,” Communications in Algebra, vol. 51, pp. 3708-3728 (2023).
[2] S. Al-Kaseasbeh and A. Erfanian, “A bipartite graph associated to elements and cosets of subgroups of a finite group,” AIMS Mathematics, vol. 6, no. 10, pp. 10395-10404 (2021).
[3] S. Al-Kaseasbeh and A. Erfanian, “The structure of Cayley graphs of dihedral groups of valencies 1, 2 and 3,” Proyecciones (Antofagasta), vol. 40, pp. 1683-1691 (2021).
[4] D. Anderson and S. Al-Kaseasbeh, “The intersection subgroup graph of a group,” Communications in Algebra, vol. 51, pp. 3556-3573 (2023).
[5] C. Berge, Graphs and Hypergraphs. Amsterdam, The Netherlands: North-Holland (1973).
[6] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications. New York, NY, USA: Elsevier (1976).
[7] A. Cayley, “The theory of groups: Graphical representation,” American Journal of Mathematics, vol. 1, no. 2, pp. 174-176 (1878), doi: 10.2307/2369306.
[8] A. Das, M. Saha, and S. Al-Kaseasbeh, “On co-maximal subgroup graph of a group,” Ricerche di Matematica, vol. 73, pp. 2075-2089 (2024), doi: 10.1007/s11587-022-00718-0.
[9] R. Diestel, Graph Theory, 5th ed. Berlin, Germany: Springer (2017).
[10] E. Dobson, H. Gavlas, J. Morris, and D. Witte, “Automorphism groups with cyclic commutator subgroup and Hamilton cycles,” Discrete Mathematics, vol. 189, no. 1-3, pp. 69-78 (Jul. 1998), doi: 10.1016/S0012-365X(98)00024-4.
[11] A. Erfanian, M. Al Tahan, and S. Al-Kaseasbeh, “Hamiltonian degree of finite groups,” International Journal of Group Theory, vol. 15, no. 4, pp. 193-206 (2026).
[12] R. W. Fitzgerald and J. Morris, “Hamiltonian paths in Cayley graphs on alternating groups,” Journal of Combinatorial Theory, Series B, vol. 97, no. 5, pp. 717-727 (2007), doi: 10.1016/j.jctb.2006.11.004.
[13] G. A. Jones and J. Morris, “Hamiltonian cycles in normal Cayley graphs,” Graphs and Combinatorics, vol. 25, pp. 389-404 (2009), doi: 10.1007/s00373-009-0835-4.
[14] K. Kuratowski, “Sur le problme des courbes gauches en topologie,” Fundamenta Mathematicae, vol. 15, pp. 271-283 (1930).
[15] J. Morris and D. Witte, “Hamiltonian cycles in Cayley graphs of small order,” Ars Mathematica Contemporanea, vol. 1, pp. 42-56 (2008), doi: 10.26493/1855-3974.41.17e.
[16] P. Siva Kota Reddy and P. S. Hemavathi, “Generalization of bipartite graphs,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 23, no. 3, pp. 787-793 (2020), doi: 10.1080/09720529.2019.1701269.
[17] S. A. Swadi and A. A. Najim, “The generalized k-connectivity of equally complete bipartite graphs and their line graphs,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 5, pp. 1567-1573 (2024), doi: 10.47974/JDMSC-1939.




