{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:BAOXQ34SAIZXKPAFRVCU2HIX55","short_pith_number":"pith:BAOXQ34S","schema_version":"1.0","canonical_sha256":"081d786f920233753c058d454d1d17ef77f35e15bb26564500edeb13e729288a","source":{"kind":"arxiv","id":"1107.4140","version":1},"attestation_state":"computed","paper":{"title":"On the metric dimension of line graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kaishun Wang, Min Feng, Min Xu","submitted_at":"2011-07-20T23:34:34Z","abstract_excerpt":"Let $G$ be a (di)graph. A set $W$ of vertices in $G$ is a \\emph{resolving set} of $G$ if every vertex $u$ of $G$ is uniquely determined by its vector of distances to all the vertices in $W$. The \\emph{metric dimension} $\\mu (G)$ of $G$ is the minimum cardinality of all the resolving sets of $G$. C\\'aceres et al. \\cite{Ca2} computed the metric dimension of the line graphs of complete bipartite graphs. Recently, Bailey and Cameron \\cite{Ba} computed the metric dimension of the line graphs of complete graphs. In this paper we study the metric dimension of the line graph $L(G)$ of $G$. In particul"},"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":"1107.4140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-20T23:34:34Z","cross_cats_sorted":[],"title_canon_sha256":"b7bbc364530828d309635dd9fb095f0f23ad35fa831c6c98c60e518352389f1c","abstract_canon_sha256":"6aaba1df21ca9f5c53bab1d39ebc761de1bb2ae6709e36c4a5bb944ac8f1c4a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:13.161525Z","signature_b64":"dhOswYWUyC/TCCnLV3n3DLaR1w2Gbdm9agrXtxmiyguDPMKRRpKgIJs7uAftIV2qrMp5of1PaURtXb3/wqgkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"081d786f920233753c058d454d1d17ef77f35e15bb26564500edeb13e729288a","last_reissued_at":"2026-05-18T04:17:13.160795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:13.160795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the metric dimension of line graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kaishun Wang, Min Feng, Min Xu","submitted_at":"2011-07-20T23:34:34Z","abstract_excerpt":"Let $G$ be a (di)graph. A set $W$ of vertices in $G$ is a \\emph{resolving set} of $G$ if every vertex $u$ of $G$ is uniquely determined by its vector of distances to all the vertices in $W$. The \\emph{metric dimension} $\\mu (G)$ of $G$ is the minimum cardinality of all the resolving sets of $G$. C\\'aceres et al. \\cite{Ca2} computed the metric dimension of the line graphs of complete bipartite graphs. Recently, Bailey and Cameron \\cite{Ba} computed the metric dimension of the line graphs of complete graphs. In this paper we study the metric dimension of the line graph $L(G)$ of $G$. In particul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4140","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":"1107.4140","created_at":"2026-05-18T04:17:13.160909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.4140v1","created_at":"2026-05-18T04:17:13.160909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4140","created_at":"2026-05-18T04:17:13.160909+00:00"},{"alias_kind":"pith_short_12","alias_value":"BAOXQ34SAIZX","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BAOXQ34SAIZXKPAF","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BAOXQ34S","created_at":"2026-05-18T12:26:24.575870+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/BAOXQ34SAIZXKPAFRVCU2HIX55","json":"https://pith.science/pith/BAOXQ34SAIZXKPAFRVCU2HIX55.json","graph_json":"https://pith.science/api/pith-number/BAOXQ34SAIZXKPAFRVCU2HIX55/graph.json","events_json":"https://pith.science/api/pith-number/BAOXQ34SAIZXKPAFRVCU2HIX55/events.json","paper":"https://pith.science/paper/BAOXQ34S"},"agent_actions":{"view_html":"https://pith.science/pith/BAOXQ34SAIZXKPAFRVCU2HIX55","download_json":"https://pith.science/pith/BAOXQ34SAIZXKPAFRVCU2HIX55.json","view_paper":"https://pith.science/paper/BAOXQ34S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.4140&json=true","fetch_graph":"https://pith.science/api/pith-number/BAOXQ34SAIZXKPAFRVCU2HIX55/graph.json","fetch_events":"https://pith.science/api/pith-number/BAOXQ34SAIZXKPAFRVCU2HIX55/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BAOXQ34SAIZXKPAFRVCU2HIX55/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BAOXQ34SAIZXKPAFRVCU2HIX55/action/storage_attestation","attest_author":"https://pith.science/pith/BAOXQ34SAIZXKPAFRVCU2HIX55/action/author_attestation","sign_citation":"https://pith.science/pith/BAOXQ34SAIZXKPAFRVCU2HIX55/action/citation_signature","submit_replication":"https://pith.science/pith/BAOXQ34SAIZXKPAFRVCU2HIX55/action/replication_record"}},"created_at":"2026-05-18T04:17:13.160909+00:00","updated_at":"2026-05-18T04:17:13.160909+00:00"}