A generalization of zero-divisor graphs

Nasehpour, Peyman

doi:10.48550/arxiv.1911.06244

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2022

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“…In [2], zero-divisor graph of a commutative ring and its properties were studied and the same were investigated for semigroups in [7]. Recently, some studies on a new family of graphs, as a generalization of zero-divisor graphs have been introduced in [11] and determined an upper-bound for the diameter of those graphs.…”

Section: Introductionmentioning

confidence: 99%

On the non-inverse graph of a group

Amreen¹,

Naduvath²

2022

Discuss. Math. - General Algebra and Applications

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Let (G, * ) be a finite group and S = {u ∈ G|u = u −1 }, then the inverse graph is defined as a graph whose vertices coincide with G such that two distinct vertices u and v are adjacent if and only if either u * v ∈ S or v * u ∈ S. In this paper, we introduce a modified version of the inverse graph, called i * -graph associated with a group G. The i * -graph is a simple graph with vertex set consisting of elements of G and two vertices x, y ∈ Γ are adjacent if x and y are not inverses of each other. We study certain properties and characteristics of this graph. Some parameters of the i *graph are also determined.

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Section: Introductionmentioning

confidence: 99%