On Generators and Undirected Cayley graphs of Γ_1-Non-Deranged Permutation Groups

Authors

  • K. O. Aremu Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria
  • F. A. Issa Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria
  • A. Muhammad Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria
  • A.R. Tasiu Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria
  • I.M. Muhammed Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria

DOI:

https://doi.org/10.57233/ijsgs.v9i2.466

Keywords:

generators, undirected cayley graphs, subnormal series, Γ_1-non deranged permutation group

Abstract

A cayley graph  of a group , where S is the set of generators of  is a graph that has a vertex for each element of  and edge  for  and . In this work, we study the
structural properties of undirected cayley graphs of the -non deranged permutation group ( ) obtained from a modulo p function (for  and  is prime), and established that the generators of  are not unique and also the undirected cayley graphs  is not simple.

Author Biographies

K. O. Aremu, Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria

Department of Mathematics, Usmanu Danfodiyo University Sokoto, P.O. Box 2346, Sokoto, Nigeria.

F. A. Issa, Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria

Department of Mathematics, Usmanu Danfodiyo University Sokoto, P.O. Box 2346, Sokoto, Nigeria.

A. Muhammad, Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria

Department of Mathematical Sciences, Federal University Gusau, P.O. Box 1001, Gusau, Nigeria.

A.R. Tasiu, Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria

Department of Mathematics, Usmanu Danfodiyo University Sokoto, P.O. Box 2346, Sokoto, Nigeria.

I.M. Muhammed, Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria

Department of Mathematics, Usmanu Danfodiyo University Sokoto, P.O. Box 2346, Sokoto, Nigeria

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Published

2023-07-31

How to Cite

Aremu, K. O. ., Issa, F. A. ., Muhammad, A., Tasiu, A. ., & Muhammed, I. . (2023). On Generators and Undirected Cayley graphs of Γ_1-Non-Deranged Permutation Groups. International Journal of Science for Global Sustainability, 9(2), 108–112. https://doi.org/10.57233/ijsgs.v9i2.466

Issue

Vol. 9 No. 2 (2023): INTERNATIONAL JOURNAL OF SCIENCE FOR GLOBAL SUSTAINABILITY

Section

Articles

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Copyright (c) 2023 Author(s)

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This work is licensed under a Creative Commons Attribution 4.0 International License.