{"paper":{"title":"Some New Results on the Curling Number of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"C. Susanth, Johan Kok, K. P. Chithra, N. K. Sudev, Sunny Joseph Kalayathankal","submitted_at":"2015-10-01T08:15:03Z","abstract_excerpt":"Let $S=S_1S_2S_3\\ldots S_n$ be a finite string. Write $S$ in the form $XYY\\ldots Y=XY^k$, consisting of a prefix $X$ (which may be empty), followed by $k$ copies of a non-empty string $Y$. Then, the greatest value of this integer $k$ is called the curling number of $S$ and is denoted by $cn(S)$. Let the degree sequence of the graph $G$ be written as a string of identity curling subsequences say, $X^{k_1}_1\\circ X^{k_2}_2\\circ X^{k_3}_3 \\ldots \\circ X^{k_l}_l$. The compound curling number of $G$, denoted $cn^c(G)$ is defined to be, $cn^n(G) = \\prod\\limits^{l}_{i=1}k_i$. In this paper, we discus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01271","kind":"arxiv","version":2},"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"}