{"paper":{"title":"All Terminal Reliability Roots of Smallest Modulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Corey D. C. DeGagn\\'e, Jason I. Brown","submitted_at":"2019-06-05T23:44:27Z","abstract_excerpt":"Given a connected graph $G$ whose vertices are perfectly reliable and whose edges each fail independently with probability $q\\in[0,1],$ the \\textit{(all-terminal) reliability} of $G$ is the probability that the resulting subgraph of operational edges contains a spanning tree (this probability is always a polynomial in $q$). The location of the roots of reliability polynomials has been well studied, with particular interest in finding those with the largest moduli. In this paper, we will discuss a related problem -- among all reliability polynomials of graphs on $n$ vertices, which has a root o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02359","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"}