International Journal of Computer
Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 4 | Year 2019 | Article Id. IJCTT-V67I4P116 | DOI : https://doi.org/10.14445/22312803/IJCTT-V67I4P116

Cayley Graph on Nilpotent Groups with and without Hamilton Path

Mohammad Badrul Alam Miah, Afroza Akter

Citation :

Mohammad Badrul Alam Miah, Afroza Akter, "Cayley Graph on Nilpotent Groups with and without Hamilton Path," International Journal of Computer Trends and Technology (IJCTT), vol. 67, no. 4, pp. 74-75, 2019. Crossref, https://doi.org/10.14445/22312803/ IJCTT-V67I4P116

Abstract

A Cayley graph that has a hamilton path as finite when every vertices are connected and does not contain Hamilton path when it is infinite has been constructed. Cayley graph must be directed and must contain nilpotent, commutator subgraph.

Keywords

Cayley graph, hamilton path, nilpotent group, commutator subgraph.

References

[1] Morris, D. W. (2011). 2-generated Cayley digraphs on nilpotent groups have hamiltonian paths. ArXiv Preprint ArXiv:1103.5293.
[2] Ghaderpour, E., & Morris, D. W. (2011). Cayley graphs on nilpotent groups with cyclic commutator subgroup are hamiltonian. ArXiv Preprint ArXiv:1111.6216.
[3] Morris, D. W. (2013). On Cayley digraphs that do not have hamiltonian paths. International Journal of Combinatorics, 2013.
[4] Morris, D. W. (2015). Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian. ArXiv Preprint ArXiv:1507.04973.