Line graphs associated to annihilating-ideal graph attached to lattices of genus one

Document Type : Research Paper


Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran


Let $(L,\wedge,\vee)$ be a lattice with a least element $0$. The annihilating-ideal graph of $L$, denoted by $\mathbb{AG}(L)$, is a graph whose vertex-set is the set of all non-trivial ideals of $L$ and, for every two distinct vertices $I$ and $J$, the vertex $I$ is adjacent to $J$ if and only if $I\wedge J=\{0\}$. In this paper, we characterize all lattices $L$ whose the graph $\mathfrak{L}(\mathbb{AG}(L))$ is toroidal.


Main Subjects

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Volume 12, Issue 4 - Serial Number 4
December 2023
Pages 175-190
  • Receive Date: 09 October 2020
  • Revise Date: 12 August 2022
  • Accept Date: 07 September 2022
  • Published Online: 01 December 2023