Gülşen ULUCAK

Çarpımsal Kafeslerde Bir Eleman ile İlgili 3-lü Sıfır Bölen Hipergrafı

? bir çarpımsal kafes ve ?,? nin bir has elemanı olsun. ? ile ilgili ? nin 3-lü sıfır bölen hipergrafını tanıttık öyle ki bu hipergrafın köşeleri{?1∈?−{?}|?1?2?3≤?⇒?1?2≰?,?2?3≰? ?? ?1?3≰? ℎ??ℎ???? ?2,?3∈?−{?} ?ç??} kümesinin elemanlarıdır ki burada ?1,?2 ve ?3 komşudur, yani, {?1,?2,?3} bu hipergarfın bir hiperkenarıdır ancak ve ancak ?1?2?3≤?⇒?1?2≰?,?2?3≰? ?? ?1?3≰?. Bu çalışma boyunca, bu hipergrafı ?3(?,?) ile göstereceğiz. Çarpımsal bir kafes üzerinde bu hipergrafın birçok özelliğini araştırdık. Ayrıca, ?3(?,?) nin diametresinin bir alt sınırını bulduk ve bu hipergrafın bağlantılı olduğunu gösterdik.

3-Zero-Divisor Hypergraph with Respect to an Element in Multiplicative Lattice

Let ? be a multiplicative lattice and ? be a proper element of ?. We introduce the 3-zero-divisor hypergraph of ? with respect to ? which is a hypergraph whose vertices are elements of the set {?1∈?−{?}|?1?2?3≤?⇒?1?2≰?,?2?3≰? ??? ?1?3≰? ??? ???? ?2,?3∈?−{?}} where distinct vertices ?1,?2 and ?3 are adjacent, that is, {?1,?2,?3} is a hyperedge if and only if ?1?2?3≤?⇒?1?2≰?,?2?3≰? ??? ?1?3≰?. Throughout this paper, the hypergraph is denoted by ?3(?,?). We investigate many properties of the hypergraph over a multiplicative lattice. Moreover, we find a lower bound of diameter of ?3(?,?) and obtain that ?3(?,?) is connected.

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