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Line graphs associated to annihilating-ideal graph attached to lattices of genus one | ||
| Transactions on Combinatorics | ||
| دوره 12، شماره 4، اسفند 2023، صفحه 175-190 اصل مقاله (501.81 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2022.125344.1771 | ||
| نویسندگان | ||
| Atossa Parsapour1؛ Khadijeh AhmadJavaheri* 2 | ||
| 1Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran | ||
| 2Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Annihilating-ideal graph؛ Genus؛ Lattice؛ Line graph؛ Toroidal graph | ||
| مراجع | ||
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