Generalized conjugacy class graph of some finite non-abelian groups

Omer, Sanaa Mohamed Saleh; Sarmin, Nor Haniza; Erfanian, Ahmad

doi:10.1063/1.4915707

Cited by 9 publications

(11 citation statements)

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“…In 2013, Moradipour et al [15] used the graph related to conjugacy classes to find some graph properties of some finite metacyclic 2-groups. The graph related to conjugacy classes was also extended by Omer et al [16], in which the vertices are orbits under the group action on a set. The following is the definition of the generalized conjugacy class graph.…”

Section: Preliminary Notesmentioning

confidence: 99%

On the probability that a group element fixes a set and its generalized conjugacy class graph

El-Sanfaz

Sarmin²,

Omer

2015

ijma

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In this paper, Ω denotes the set of all subsets of commuting elements of G in the form of (a, b), where a and b commute, |a| = |b| = 2. The probability that a group element of G fixes a set is one of the generalizations of the commutativity degree that has been recently introduced. In this paper, the probability that an element of a group fixes a set for semi-dihedral groups and quasi-dihedral groups is found. The results obtained are then applied to graph theory, more precisely to the generalized conjugacy class graph.Mathematics Subject Classification: 20P05, 20B40, 97K30

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Section: Preliminary Notesmentioning

confidence: 99%

On the probability that a group element fixes a set and its generalized conjugacy class graph

El-Sanfaz

Sarmin²,

Omer

2015

ijma

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“…G A pair of vertices of this graph are connected by an edge if their cardinalities are not coprime. Omer et al [9] extended the work on conjugacy class graph by defining the generalized conjugacy class graph whose vertices are non-central orbits in which two vertices are adjacent if their cardinalities are not coprime.…”

Section: In Gmentioning

confidence: 99%

Groups and graphs in probability theory

Sarmin¹,

El-Sanfaz

Omer

2016

AIP Conference Proceedings

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Abstract. In this paper, G denotes a dihedral group of order 2n and 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 2. a bBy 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 under regular action is computed. The results obtained are then applied to graph theory, more precisely to generalized conjugacy class graph and orbit graph.

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“…Later on, Omer et al [24] generalized the conjugacy class graph, where the vertices are orbits under the group action on a set. The definition of the generalized conjugacy class graph is stated in the following.…”

Section: G G S Gs S G G S S P S S Gmentioning

confidence: 99%