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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Main Authors: Sarmin, N. H., El-Sanfaz, M. A., Omer, S. M. S.
Format: Conference or Workshop Item
Published: American Institute of Physics Inc. 2016
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Online Access: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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Institution: Universiti Teknologi Malaysia
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spelling 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
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
spellingShingle QA Mathematics
Sarmin, N. H.
El-Sanfaz, M. A.
Omer, S. M. S.
Groups and graphs in probability theory
description 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
url 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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