{"paper":{"title":"Peaks on Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Diaz-Lopez, Erik Insko, Lucas Everham, Mohamed Omar, Pamela E. Harris, Vincent Marcantonio","submitted_at":"2017-08-28T19:20:28Z","abstract_excerpt":"Given a graph $G$ with $n$ vertices and a bijective labeling of the vertices using the integers $1,2,\\ldots, n$, we say $G$ has a peak at vertex $v$ if the degree of $v$ is greater than or equal to 2, and if the label on $v$ is larger than the label of all its neighbors. Fix an enumeration of the vertices of $G$ as $v_1,v_2,\\ldots, v_{n}$ and a fix a set $S\\subset V(G)$. We want to determine the number of distinct bijective labelings of the vertices of $G$, such that the vertices in $S$ are precisely the peaks of $G$. The set $S$ is called the \\emph{peak set of the graph} $G$, and the set of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08493","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"}