On the power graphs of certain finite groups

Ali, Fawad; Fatima, S. Firthous; Wang, Wei

doi:10.1080/03081087.2020.1856028

Cited by 10 publications

(8 citation statements)

References 22 publications

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“…A remarkable feature of

is that the involution

and the identity e are adjacent to every other node in their power graph. Several researchers [ 29 , 30 , 31 , 32 ] have analyzed the complete description of the above-mentioned groups and their power graphs. The first survey paper on power graphs was published in 2013 [ 33 ], and the most recent study was [ 34 ].…”

Section: Basic Notions and Notationsmentioning

confidence: 99%

Power Graphs of Finite Groups Determined by Hosoya Properties

Ali

Rather

Din

et al. 2022

Entropy

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Suppose G is a finite group. The power graph represented by P(G) of G is a graph, whose node set is G, and two different elements are adjacent if and only if one is an integral power of the other. The Hosoya polynomial contains much information regarding graph invariants depending on the distance. In this article, we discuss the Hosoya characteristics (the Hosoya polynomial and its reciprocal) of the power graph related to an algebraic structure formed by the symmetries of regular molecular gones. As a consequence, we determined the Hosoya index of the power graphs of the dihedral and the generalized groups. This information is useful in determining the renowned chemical descriptors depending on the distance. The total number of matchings in a graph Γ is known as the Z-index or Hosoya index. The Z-index is a well-known type of topological index, which is popular in combinatorial chemistry and can be used to deal with a variety of chemical characteristics in molecular structures.

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“…A remarkable feature of

is that the involution

Section: Basic Notions and Notationsmentioning

confidence: 99%

Power Graphs of Finite Groups Determined by Hosoya Properties

Ali

Rather

Din

et al. 2022

Entropy

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“…Throughout this paper, the power graph for the dihedral group is denoted by Γ D 2n . It is clear that Γ D 2n is a connected graph [2].…”

Section: Introductionmentioning

confidence: 99%

“…Kumar et al [7] have presented a complete and excellent survey of the power graph for some finite groups. Meanwhile, the degree of Γ D 2n has been presented by [2] as in the following theorem: Theorem 1. [2] If Γ D 2n is the power graph of D 2n , then (i) the degree of a in Γ D 2n is d e = 2n − 1,…”

Section: Introductionmentioning

confidence: 99%

Spectral Properties of Power Graph of Dihedral Groups

Romdhini,

Nawawi,

Al-Sharqi

et al. 2024

Eur. J. Pure Appl. Math.

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“…The first review of the power graph was published in 2013 [16] , and the latest review was published in 2021 [17] . Moreover, many researchers investigated other algebraic graph concepts, such as [18] , [19] , [20] .…”

Section: Introductionmentioning

confidence: 99%

Several Zagreb indices of power graphs of finite non-abelian groups

Ismail,

Ali,

Qasim

et al. 2023

Heliyon

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On the power graphs of certain finite groups

Cited by 10 publications

References 22 publications

Power Graphs of Finite Groups Determined by Hosoya Properties

Power Graphs of Finite Groups Determined by Hosoya Properties

Spectral Properties of Power Graph of Dihedral Groups

Several Zagreb indices of power graphs of finite non-abelian groups

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