Graphs, partitions and classes of groups

Ballester‐Bolinches, A.; Cossey, John

doi:10.1007/s00605-010-0263-3

Cited by 6 publications

(3 citation statements)

References 20 publications

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“…In the past few decades, several graphs have been constructed from algebraic structures based on different properties possessed by the algebraic structures, and these algebraic graphs have been studied extensively, in order to understand the algebraic structure more clearly, thereby making this an enthralling area of research (c.f. [2][3][4][5][6][7]).…”

Section: Introductionmentioning

confidence: 99%

Graphs Defined on Rings: A Review

Madhumitha,

Naduvath

2023

Mathematics

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The study on graphs emerging from different algebraic structures such as groups, rings, fields, vector spaces, etc. is a prominent area of research in mathematics, as algebra and graph theory are two mathematical fields that focus on creating and analysing structures. There are numerous studies linking algebraic structures and graphs, which began with the introduction of Cayley graphs of groups. Several algebraic graphs have been defined on rings, a fast-growing area in the literature. In this article, we systematically review the literature on some variants of Cayley graphs that are defined on rings and highlight the properties and characteristics of such graphs, to showcase the research in this area.

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Section: Introductionmentioning

confidence: 99%

Graphs Defined on Rings: A Review

Madhumitha,

Naduvath

2023

Mathematics

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“…These differences lie in the adjacency criterion used to relate two group elements constituting the set of vertices of such a graph. Some essential authors in this context are A. Abdollahi [3], A. Ballester-Bolinches et al [4][5][6][7][8], A. Lucchini [9,10], and D. Hai-Reuven [11], among others.…”

Section: Introductionmentioning

confidence: 99%

The t-Graphs over Finitely Generated Groups and the Minkowski Metric

2022

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“…The investigation of graphs related to groups as well as other algebraic structures is an exciting research topic in the last few decades, [1,2,3,4,5,6,9,11,14,16,17,18]. Only basic concepts about graphs will be needed for this paper.…”

Section: Introductionmentioning

confidence: 99%

The enhanced quotient graph of the quotient of a finite group

Dupont¹,

Mendoza²,

Rodríguez³

2017

Preprint

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For a finite group G with a normal subgroup H, the enhanced quotient graph of G/H, denoted by G H (G), is the graph with vertex set V = (G\H) ∪ {e} and two vertices x and y are edge connected if xH = yH or xH, yH ∈ zH for some z ∈ G. In this article, we characterize the enhanced quotient graph of G/H. The graph G H (G) is complete if and only if G/H is cyclic, and G H (G) is Eulerian if and only if |G/H| is odd. We show some relation between the graph G H (G) and the enhanced power graph G(G/H) that was introduced by Sudip Bera and A.K. Bhuniya (2016). The graph G H (G) is complete if and only if G/H is cyclic if and only if G(G/H) is complete. The graph G H (G) is Eulerian if and only if |G| is odd if and only if G(G) is Eulerian, i.e., the property of being Eulerian does not depend on the normal subgroup H.

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Graphs, partitions and classes of groups

Cited by 6 publications

References 20 publications

Graphs Defined on Rings: A Review

Graphs Defined on Rings: A Review

The t-Graphs over Finitely Generated Groups and the Minkowski Metric

The enhanced quotient graph of the quotient of a finite group

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