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In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on $n$ vertices, and propose an open problem for further research."},"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":"1404.0931","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-04-03T14:26:20Z","cross_cats_sorted":[],"title_canon_sha256":"3c4699e3a4a8d625ede57a61df3ebdd1aa0aadc35d1c4f60144534ab47bd92c1","abstract_canon_sha256":"e5f6a0c1606e63c4f8b440940bc793144b4d38bc76997e7751a3d6d1f3a9efdb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:54.991608Z","signature_b64":"AbrknjwhEsP/hOMOjCAtfCKAjNIXOf00VLIzV8pRuX2HvqgWOHSt2zPMcT9tMBQJ9J/xqt6ejTx9aV7PKrlwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1a9c868a1659add89668241dc8c3bee98e0c472617934babb6a49ef68caeb24","last_reissued_at":"2026-05-18T02:54:54.991102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:54.991102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Minimal Total Irregularity of Graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jieshan Yang, Lihua You, Yingxue Zhu","submitted_at":"2014-04-03T14:26:20Z","abstract_excerpt":"In \\cite{2012a}, Abdo and Dimitov defined the total irregularity of a graph $G=(V,E)$ as\n  \\hskip3.3cm $\\rm irr_{t}$$(G) = \\frac{1}{2}\\sum_{u,v\\in V}|d_{G}(u)-d_{G}(v)|, $\n  \\noindent where $d_{G}(u)$ denotes the vertex degree of a vertex $u\\in V$. 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