The k-maximal hypergraph of commutative rings

Autor: K. Selvakumar, V. C. Amritha
Rok vydání: 2020
Předmět:
Zdroj: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 61:747-757
ISSN: 2191-0383
0138-4821
Popis: Let R be a commutative ring with identity, $$k\ge 2$$ a fixed integer and $$\mathcal {I}(R,k)$$ be the set of all k-maximal elements in R. The k-maximal hypergraph associated with R, denoted by $$\mathcal {H}^k(R)$$ , is a hypergraph with the vertex set $$\mathcal {I}(R, k)$$ and for distinct elements $$a_1, a_2,\ldots , a_k$$ in $$\mathcal {I}(R, k)$$ the set $$\{a_1, a_2,\ldots , a_k\}$$ is an edge of $$\mathcal {H}^k(R)$$ if and only if $$\sum \nolimits _{i=1}^{k} Ra_{i}=R$$ and for all $$1\le j\le k$$ . In this paper, the connectedness, diameter and girth of $$\mathcal {H}^k(R)$$ are studied. Moreover, the regularity and coloring of $$\mathcal {H}^k(R)$$ are investigated. Among other things, we characterize all finite commutative rings R for which the k-maximal hypergraph $$\mathcal {H}^k(R)$$ is outerplanar and planar.
Databáze: OpenAIRE
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