{"paper":{"title":"Some physical and chemical indices of clique-inserted-lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Zuhe Zhang","submitted_at":"2013-02-24T17:43:52Z","abstract_excerpt":"The operation of replacing every vertex of an $r$-regular lattice $H$ by a complete graph of order $r$ is called clique-inserting, and the resulting lattice is called the clique-inserted-lattice of $H$. For any given $r$-regular lattice, applying this operation iteratively, an infinite family of $r$-regular lattices is generated. Some interesting lattices including the 3-12-12 lattice can be constructed this way. In this paper, we reveal the relationship between the energy and resistance distance of an $r$-regular lattice and that of its clique-inserted-lattice. As an application, the asymptot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5932","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}