biostudies-literatureWei YScience Fund for Distinguished Young Scholars of Hunan Province of ChinaYouth Science and Technology Talent Project of Hunan ProvinceResearch Foundation of Education Bureau of Hunan Province ChinaNational Natural Science Foundation of China523-530https://www.ebi.ac.uk/biostudies/studies/S-EPMC12403172biostudies-literatureUnknown12(Pt 5)Post-graphite in cold-compression [Mao et al. (2003). Science 302, 425-427] has attracted widespread research interest in condensed matter physics. Subsequently, many low-energy carbon phases, such as M-carbon, W-carbon and Z-carbon, have been proposed as structural candidates. Based on graph theory, we found that these 4-coordinated post-graphite candidates can not only be decomposed into 3-regular graphitic graphs but also yield (2+1)-regular graphs in a non-graphitic manner from different decomposition directions. This inspires a general idea of generating 3D 4-coordinate networks based on 2D (2+1)-regular bipartite-like graphs, which can be efficiently generated by a random method combined with group and graph theory (RG2). Associated with such a general graph-based method, a large numIUCrJLow-energy tetrahedral networks for carbon and silicon from (2+1)-regular bipartite-like graphs.PMC12403172523722601237404623A0102122043972022RC11972024JJ2048He CLi SWei YShi XfalseLow-energy tetrahedral networks for carbon and silicon from (2+1)-regular bipartite-like graphs.Post-graphite in cold-compression [Mao et al. (2003). Science 302, 425-427] has attracted widespread research interest in condensed matter physics. Subsequently, many low-energy carbon phases, such as M-carbon, W-carbon and Z-carbon, have been proposed as structural candidates. Based on graph theory, we found that these 4-coordinated post-graphite candidates can not only be decomposed into 3-regular graphitic graphs but also yield (2+1)-regular graphs in a non-graphitic manner from different decomposition directions. This inspires a general idea of generating 3D 4-coordinate networks based on 2D (2+1)-regular bipartite-like graphs, which can be efficiently generated by a random method combined with group and graph theory (RG2). Associated with such a general graph-based method, a large num2025-01-01T00:00:00Z2025 Sep2026-05-29T16:57:49.635Z2026-04-08T05:28:56.476ZS-EPMC124031724072839210.1107/S2052252525005810