Sağlam, Derya2025-01-212025-01-2120222473-6988https://doi.org/10.3934/math.2022946https://hdl.handle.net/20.500.12587/23465In this paper, homothetical and translation lightlike graphs, which are generalizations of homothetical and translation lightlike hypersurfaces are investigated in the semi-Euclidean space Rn+2 q, respectively. We prove that all homothetical and all translation lightlike graphs are locally the hyperplanes. According to this fact, both of these graphs are minimal. © 2022 the Author(s), licensee AIMS Press.eninfo:eu-repo/semantics/openAccesshomothetical graphs; lightlike hypersurfaces; minimality; semi-Euclidean space; translation graphsArticle79171981720910.3934/math.20229462-s2.0-85134614693Q1