Relative non nil-n graphs of finite groups

Erfanian, Ahmad; Haghighi, Behnaz Tolue

doi:10.2306/scienceasia1513-1874.2012.38.201

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…There are many ways to associate a graph to a group [1][2][3][4] . In this paper, we consider the noncommuting graph of a metacyclic p-group G which is denoted by Γ G .…”

Section: Introductionmentioning

confidence: 99%

Some results on the non-commuting graph of a finite group

Moradipour¹,

Ilangovanb²,

Rashidc³

2019

ScienceAsia

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Let G be a metacyclic p-group, and let Z(G) be its center. The non-commuting graph Γ G of a metacyclic pgroup G is defined as the graph whose vertex set is G−Z(G), and two distinct vertices x and y are connected by an edge if and only if the commutator of x and y is not the identity. In this paper, we give some graph theoretical properties of the non-commuting graph Γ G . Particularly, we investigate planarity, completeness, clique number and chromatic number of such graph. Also, we prove that if G 1 and G 2 are isoclinic metacyclic p-groups, then their associated graphs are isomorphic.

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“…There are many ways to associate a graph to a group [1][2][3][4] . In this paper, we consider the noncommuting graph of a metacyclic p-group G which is denoted by Γ G .…”

Section: Introductionmentioning

confidence: 99%

Some results on the non-commuting graph of a finite group

Moradipour¹,

Ilangovanb²,

Rashidc³

2019

ScienceAsia

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“…This concept was first introduce by Erfanian et al in [5]. Meanwhile, in 2011, Erfanian et al [6] defined the relative n-th commutativity degree as the probability that the n-th power of a random element of H commutes with a random element of G. This relative commutativity degree can be extended to the productivity degree of two subgroups of G where it is defined as the ratio of the order of the intersection of HK and KH with the order of their union where H and K are the subgroups of a group G | | Pro ( , ) .…”

Section: Introductionmentioning

confidence: 99%

The productivity degree of two subgroups of dihedral groups

Hamid

Ali²,

Sarmin³

et al. 2014

AIP Conference Proceedings

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The relative commutativity degree of noncyclic subgroups of nonabelian metabelian groups of order at most 14 AIP Conference Proceedings 1870, 030005 (2017) Abstract. The commutativity degree of a group is the probability that two randomly chosen elements of G commute. The concept of commutativity degree is then extended to the relative commutativity degree of a group, which is defined as the probability for an element of H and an element of G to commute to one another. In this research, the relative commutativity degree concept is extended to the probability of a product of two subgroups of a group G productivity degree of two subgroups of a group G which is defined as the ratio of the order of the intersection of HK and KH with the order of their union where H and K are the subgroups of a group G. This research focuses only on the dihedral groups.

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“…A few years later, Erfanian et al [4] gave the relative case of n-th commutativity degree. They identify the probability that the n-th power of a random element of a subgroup, H commutes with another random element of a group G, denoted as P n (H,G).…”

Section: Introductionmentioning

confidence: 99%