On the Essential Element Graph of a Lattice
Turkish Journal of Mathematics and Computer Science, cilt.14, sa.2, ss.248-255, 2022 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 2
- Basım Tarihi: 2022
- Doi Numarası: 10.47000/tjmcs.885881
- Dergi Adı: Turkish Journal of Mathematics and Computer Science
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.248-255
- İstanbul Kültür Üniversitesi Adresli: Evet
Özet
Let $mathcal{L}$ be a bounded lattice. The essential element graph of $mathcal{L}$ is a simple undirected graph $varepsilon_{mathcal{L}}$ such that the elements $x,y$ of $mathcal{L}$ form an edge in $varepsilon_{mathcal{L}}$, whenever $x vee y $ is an essential element of $mathcal{L}$. In this paper, we study properties of the essential elements of lattices and essential element graphs. We study the lattices whose zero-divisor graphs and incomparability graphs are isomorphic to its essential element graphs. Moreover, the line essential element graphs are investigated.