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Here, we characterize the non-regular graphs with minimal total irregularity and thereby resolve the recent conjecture by Zhu, You and Yang~\\cite{zyy-mtig-2014} about the lower bound on the minimal total irregularity of non-regular connected graphs. We show that the conjectured lower bound of $2n-4$ is attained only i"},"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":"1407.1276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-04T17:04:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b1b5d2aaaaabedd54668202e099aab5fa6f3eadfbdaadcf507e8082459c6d73d","abstract_canon_sha256":"33eeec0fc808c4d41c3fab859d17d097b8c1f4ad5358d178f4f45034bd5a965c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:18.220246Z","signature_b64":"ztYdpxpc3vd2OrAa319bbc/s72T2ufaNe4Te5UmGSgfG9t/mw3qca7mZKTX5SMzpRYr5NK/xOO6EgFmofoXUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43b8907fd1a52c0ed3a6765a8eea38c5ac81420a0338ece8dc4c4453209ce57d","last_reissued_at":"2026-05-18T02:48:18.219783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:18.219783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-regular graphs with minimal total irregularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Darko Dimitrov, Hosam Abdo","submitted_at":"2014-07-04T17:04:17Z","abstract_excerpt":"The {\\it total irregularity} of a simple undirected graph $G$ is defined as ${\\rm irr}_t(G) =$ $\\frac{1}{2}\\sum_{u,v \\in V(G)}$ $\\left| d_G(u)-d_G(v) \\right|$, where $d_G(u)$ denotes the degree of a vertex $u \\in V(G)$. Obviously, ${\\rm irr}_t(G)=0$ if and only if $G$ is regular. Here, we characterize the non-regular graphs with minimal total irregularity and thereby resolve the recent conjecture by Zhu, You and Yang~\\cite{zyy-mtig-2014} about the lower bound on the minimal total irregularity of non-regular connected graphs. We show that the conjectured lower bound of $2n-4$ is attained only i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1276","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.1276","created_at":"2026-05-18T02:48:18.219851+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.1276v1","created_at":"2026-05-18T02:48:18.219851+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1276","created_at":"2026-05-18T02:48:18.219851+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IO4JA76RUUWA5U5GOZNI52RYYW","json":"https://pith.science/pith/IO4JA76RUUWA5U5GOZNI52RYYW.json","graph_json":"https://pith.science/api/pith-number/IO4JA76RUUWA5U5GOZNI52RYYW/graph.json","events_json":"https://pith.science/api/pith-number/IO4JA76RUUWA5U5GOZNI52RYYW/events.json","paper":"https://pith.science/paper/IO4JA76R"},"agent_actions":{"view_html":"https://pith.science/pith/IO4JA76RUUWA5U5GOZNI52RYYW","download_json":"https://pith.science/pith/IO4JA76RUUWA5U5GOZNI52RYYW.json","view_paper":"https://pith.science/paper/IO4JA76R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.1276&json=true","fetch_graph":"https://pith.science/api/pith-number/IO4JA76RUUWA5U5GOZNI52RYYW/graph.json","fetch_events":"https://pith.science/api/pith-number/IO4JA76RUUWA5U5GOZNI52RYYW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IO4JA76RUUWA5U5GOZNI52RYYW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IO4JA76RUUWA5U5GOZNI52RYYW/action/storage_attestation","attest_author":"https://pith.science/pith/IO4JA76RUUWA5U5GOZNI52RYYW/action/author_attestation","sign_citation":"https://pith.science/pith/IO4JA76RUUWA5U5GOZNI52RYYW/action/citation_signature","submit_replication":"https://pith.science/pith/IO4JA76RUUWA5U5GOZNI52RYYW/action/replication_record"}},"created_at":"2026-05-18T02:48:18.219851+00:00","updated_at":"2026-05-18T02:48:18.219851+00:00"}