Ranks, Subdegrees and Suborbital graphs of the product action of Affine Groups

Authors

  • Siahi Maxwell Agwanda Department of Mathematics, Kenyatta University, P.O. Box 43844-00100, Nairobi
  • Patrick Kimani Department of Mathematics and Computer science, University of Kabianga, P.O. Box 2030-20200, Kericho
  • Ireri Kamuti Department of Mathematics, Kenyatta University, P.O. Box 43844-00100, Nairobi

DOI:

https://doi.org/10.24297/jam.v19i.8891

Keywords:

Transitivity and Suborbital graphs, Subdegrees, Ranks

Abstract

The action of affine groups on Galois field has been studied.  For instance,  studied the action of on Galois field for  a power of prime.  In this paper, the rank and subdegree of the direct product of affine groups over Galois field acting on the cartesian product of Galois field is determined. The application of the definition of the product action is used to achieve this. The ranks and subdegrees are used in determination of suborbital graph, the non-trivial suborbital graphs that correspond to this action have been constructed using Sims procedure and were found to have a girth of 0, 3, 4 and 6.

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References

Armstrong, M. A. (2013). Groups and symmetry. Springer Science and Business Media.

Kamuti, I. N., Inyangala, E. B., & Rimberia, J. K. (2012). Action of on and the Corresponding Suborbital Graphs. In International Mathematical Forum 7(30), 1483-1490.

Kangogo, M.R. (2015). Ranks and Subdegrees of the cyclic group of affine group and the associated suborbital graphs. Ph.D., Mathematical studies.

Magero, F. B. (2015). Cycle indices, sub degrees and suborbital graphs of PSL(2,q) acting on the cosets of some of its subgroups. Ph.d, Mathematical studies

Mizzi, J. L. R., & Scapellato, R. (2011). Two-fold automorphisms of graphs. Australasian Journal of Combinatorics, 49, 165-176.

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Published

2020-11-09

How to Cite

Agwanda, S. M. ., Kimani, P., & Kamuti, I. . (2020). Ranks, Subdegrees and Suborbital graphs of the product action of Affine Groups. JOURNAL OF ADVANCES IN MATHEMATICS, 19, 99-106. https://doi.org/10.24297/jam.v19i.8891

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