Line graphs associated to annihilating-ideal graph attached to lattices of genus one
نویسندگان
1 Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran
2 Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran
doi
10.22108/toc.2022.125344.1771چکیده
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.
