University of Guilan Journal of Algebra and Related Topics 2345-3931 2026 02 19 Identity meet graph of elements of lattices 9457 10.22124/jart.2026.29711.1766 EN Sh. Ebrahimi Atani Department of Pure Mathematics, University of Guilan, Rasht, Iran 0009-0001-2215-9640 Journal Article 2025 01 30 Let $\mathcal{L}$ be a complete lattice. The identity meet graph of elements of $\mathcal{L}$, denoted by $\mathbb{IMG} (\mathcal{L})$, is an undirected simple graph whose vertices are all nontrivial elements of $\mathcal{L}$ and two distinct elements $x$ and $y$ are adjacent if and only if $x \vee y = 1$ and $x \wedge y \neq 0$. The basic properties and possible structures of the graph $\mathbb{IMG}(\mathcal{L})$ are investigated. The connectedness, clique number, domination number, independence number, chromatic number of $\mathbb{IMG}(\mathcal{L})$ and their relations to algebraic properties of $\mathcal{L}$ are explored. https://jart.guilan.ac.ir/article_9457_d57f2631adfcf3db1b08a95f67e6a7e7.pdf