Perfect unit graphs of commutative Artinian rings

Mirghadim, S. M. Saadat; Nikandish, Reza; Nikmehr, M. J.

doi:10.1007/s13370-020-00868-0

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Unit Graph Of a Ring1

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2023

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“…Using this result, the parameters were computed and the final result was proven. This discussion of the weak perfect property led to the discussion of the property of perfection in the unit graphs of rings in [228], where the perfection of the unit graphs of finite commutative Artinian rings were examined and the results on classification of rings whose unit graphs were perfect and not-perfect were obtained.…”

Section: Unit Graph Of a Ringmentioning

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: Unit Graph Of a Ringmentioning

confidence: 99%