Groups and graphs in probability theory
In this paper, G denotes a dihedral group of order 2n and Ω denotes the set of all subsets of all commuting elements of size two in the form of (a,b), where a and b commute and |a| = |b| = 2. By extending the concept of commutativity degree, the probability that an element of a group fixes a set can...
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American Institute of Physics Inc.
2016
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my.utm.732162017-11-27T02:00:04Z http://eprints.utm.my/id/eprint/73216/ Groups and graphs in probability theory Sarmin, N. H. El-Sanfaz, M. A. Omer, S. M. S. QA Mathematics In this paper, G denotes a dihedral group of order 2n and Ω denotes the set of all subsets of all commuting elements of size two in the form of (a,b), where a and b commute and |a| = |b| = 2. By extending the concept of commutativity degree, the probability that an element of a group fixes a set can be acquired using the group actions on set. In this paper, the probability that an element of G fixes the set Ω under regular action is computed. The results obtained are then applied to graph theory, more precisely to generalized conjugacy class graph and orbit graph. American Institute of Physics Inc. 2016 Conference or Workshop Item PeerReviewed Sarmin, N. H. and El-Sanfaz, M. A. and Omer, S. M. S. (2016) Groups and graphs in probability theory. In: 23rd Malaysian National Symposium of Mathematical Sciences: Advances in Industrial and Applied Mathematics, SKSM 2015, 24 November 2015 through 26 November 2015, Johor Bahru; Malaysia. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84984570554&doi=10.1063%2f1.4954600&partnerID=40&md5=9f243f2c4a8a625fb47d8a059086bb00 |
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QA Mathematics Sarmin, N. H. El-Sanfaz, M. A. Omer, S. M. S. Groups and graphs in probability theory |
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In this paper, G denotes a dihedral group of order 2n and Ω denotes the set of all subsets of all commuting elements of size two in the form of (a,b), where a and b commute and |a| = |b| = 2. By extending the concept of commutativity degree, the probability that an element of a group fixes a set can be acquired using the group actions on set. In this paper, the probability that an element of G fixes the set Ω under regular action is computed. The results obtained are then applied to graph theory, more precisely to generalized conjugacy class graph and orbit graph. |
| format |
Conference or Workshop Item |
| author |
Sarmin, N. H. El-Sanfaz, M. A. Omer, S. M. S. |
| author_facet |
Sarmin, N. H. El-Sanfaz, M. A. Omer, S. M. S. |
| author_sort |
Sarmin, N. H. |
| title |
Groups and graphs in probability theory |
| title_short |
Groups and graphs in probability theory |
| title_full |
Groups and graphs in probability theory |
| title_fullStr |
Groups and graphs in probability theory |
| title_full_unstemmed |
Groups and graphs in probability theory |
| title_sort |
groups and graphs in probability theory |
| publisher |
American Institute of Physics Inc. |
| publishDate |
2016 |
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http://eprints.utm.my/id/eprint/73216/ https://www.scopus.com/inward/record.uri?eid=2-s2.0-84984570554&doi=10.1063%2f1.4954600&partnerID=40&md5=9f243f2c4a8a625fb47d8a059086bb00 |
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