{"paper":{"title":"A Description of the Subgraph Induced at a Labeling of a Graph by the Subset of Vertices with an Interval Spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Arpine M. Khachatryan, Narine N. Davtyan, Rafayel R. Kamalian","submitted_at":"2014-10-29T10:54:11Z","abstract_excerpt":"The sets of vertices and edges of an undirected, simple, finite, connected graph $G$ are denoted by $V(G)$ and $E(G)$, respectively. An arbitrary nonempty finite subset of consecutive integers is called an interval. An injective mapping $\\varphi:E(G)\\rightarrow \\{1,2,...,|E(G)|\\}$ is called a labeling of the graph $G$. If $G$ is a graph, $x$ is its arbitrary vertex, and $\\varphi$ is its arbitrary labeling, then the set $S_G(x,\\varphi)\\equiv\\{\\varphi(e)/ e\\in E(G), e \\textrm{is incident with} x$\\} is called a spectrum of the vertex $x$ of the graph $G$ at its labeling $\\varphi$. For any graph $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7927","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"}