On the generalized commuting and non-commuting graph for metacyclic 3-groups
DOI:
https://doi.org/10.11113/mjfas.v13n3.618Keywords:
Metacyclic 3-Groups, Commuting Graph, Non-Commuting Graph, CommuteAbstract
Let be a metacyclic 3-group and let be a non-empty subset of such that . The generalized commuting and non-commuting graphs of a group is denoted by and respectively. The vertex set of the generalized commuting and non-commuting graphs are the non-central elements in the set such that where Two vertices in are joined by an edge if they commute, meanwhile, the vertices in are joined by an edge if they do not commute.References
Basri, A. M. A. 2013. Capability and homological functors of finite metacyclic p-groups. Doctor Philosophy, Universiti Teknologi Malaysia.
Rotman, J. J. 2002. Advanced modern algebra. (1stEdition). Upper Saddle River, N.J.: Prentice Hall.
Omer, S. M. S., Sarmin, N. H., Erfanian, A., Moradipour, K. 2013. The probability that an element of a group fixes a set and and the group act on a set by conjugation. International Journal of Applied Mathematics and Statistics. 32(2), 111-117.
Goodman, F. M. 1998. Algebra: Abstract and Concrete. Upper Saddle River, N.J.: Prentice Hall.
El-Sanfaz, M. A. 2016. The Probability that an element of a non-abelian group fixes a set and its applications in graph theory. Doctor Philosophy, Universiti Teknologi Malaysia.
