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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.01271","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-10-01T08:15:03Z","cross_cats_sorted":[],"title_canon_sha256":"577fcb1b57dbe84c3b5d9f2685ade46e6b31199119a3d394ad0d9a4d3de144cb","abstract_canon_sha256":"2366ecf84c04e6b4e68ed1724f6942566c3cb6d9f4565273e6843a3742c526f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:36.430219Z","signature_b64":"uphTJ5Gv4USZ6lD4y9FiXowaH3zi0F3TlXzpInPHyHaRjNW2RKje+t2Z0vFMrqtresU8MDl7nHRK61f99KUnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9027ebb6698e5f62a0a96178ddf182b4c9c67a8495c24ea84a45d30d556cb29","last_reissued_at":"2026-05-18T01:09:36.429836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:36.429836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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, $cn^n(G) = \\prod\\limits^{l}_{i=1}k_i$. 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