{"paper":{"title":"On a Construction of Integrally Invertible Graphs and their Spectral Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Sevcovic, Sona Pavlikova","submitted_at":"2017-07-05T05:44:17Z","abstract_excerpt":"Godsil (1985) defined a graph to be invertible if it has a non-singular adjacency matrix whose inverse is diagonally similar to a nonnegative integral matrix; the graph defined by the last matrix is then the inverse of the original graph. In this paper we call such graphs positively invertible and introduce a new concept of a negatively invertible graph by replacing the adjective `nonnegative' by `nonpositive in Godsil's definition; the graph defined by the negative of the resulting matrix is then the negative inverse of the original graph. We propose new constructions of integrally invertible"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02210","kind":"arxiv","version":1},"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"}