{"paper":{"title":"More Circulant Graphs exhibiting Pretty Good State Transfer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hiranmoy Pal","submitted_at":"2017-05-24T16:50:00Z","abstract_excerpt":"The transition matrix of a graph $G$ corresponding to the adjacency matrix $A$ is defined by $H(t):=\\exp{\\left(-itA\\right)},$ where $t\\in\\mathbb{R}$. The graph is said to exhibit pretty good state transfer between a pair of vertices $u$ and $v$ if there exists a sequence $\\left\\lbrace t_k\\right\\rbrace$ of real numbers such that $\\lim\\limits_{k\\rightarrow\\infty} H(t_k) {\\bf e}_u=\\gamma {\\bf e}_v$, where $\\gamma$ is a complex number of unit modulus. We classify some circulant graphs exhibiting or not exhibiting pretty good state transfer. This generalize several pre-existing results on circulant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08859","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"}