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The alternating group graph $AG_n$, extended alternating group graph $EAG_n$ and complete alternating group graph $CAG_n$ are the Cayley graphs $\\mathrm{Cay}(A_n,T_1)$, $\\mathrm{Cay}(A_n,T_2)$ and $\\mathrm{Cay}(A_n,T_3)$, respectively, where $T_1=\\{(1,2,i),(1,i,2)\\mid 3\\leq i\\leq n\\}$, $T_2=\\{(1,i,j),(1,j,i)\\mid 2\\leq i<j\\leq n\\}$ and $T_3=\\{(i,j,k),(i,k,j)\\mid 1\\leq i<j<k\\leq n\\}$. In this paper, we determine the second largest eigenvalues of $AG_n$, $EAG_n$ and $CAG_n$."},"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":"1711.08944","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-24T12:31:27Z","cross_cats_sorted":[],"title_canon_sha256":"160bd998afa6832c043ba21abaa0edada7ebd40e6379caafb8c1d12c2f5c9950","abstract_canon_sha256":"6f7724c7cc2cbee569a8730555442683421ec28607776bb153293d5dc196c454"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:31.098586Z","signature_b64":"UZ1XWDf6T3Q3saBTVOd5PXYq2D+QWx28kxgNFvL3kOsKmSP1PFL8u28u6fvmW39lJ4IhMORxviZs5czHVOOMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ae8e69feefc5a85d80f41ab97273ac7604a2de16c61688421db7ffe87a27c13","last_reissued_at":"2026-05-17T23:58:31.097982Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:31.097982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The second largest eigenvalues of some Cayley graphs on alternating groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Qiongxiang Huang, Xueyi Huang","submitted_at":"2017-11-24T12:31:27Z","abstract_excerpt":"Let $A_n$ denote the alternating group of degree $n$ with $n\\geq 3$. The alternating group graph $AG_n$, extended alternating group graph $EAG_n$ and complete alternating group graph $CAG_n$ are the Cayley graphs $\\mathrm{Cay}(A_n,T_1)$, $\\mathrm{Cay}(A_n,T_2)$ and $\\mathrm{Cay}(A_n,T_3)$, respectively, where $T_1=\\{(1,2,i),(1,i,2)\\mid 3\\leq i\\leq n\\}$, $T_2=\\{(1,i,j),(1,j,i)\\mid 2\\leq i<j\\leq n\\}$ and $T_3=\\{(i,j,k),(i,k,j)\\mid 1\\leq i<j<k\\leq n\\}$. In this paper, we determine the second largest eigenvalues of $AG_n$, $EAG_n$ and $CAG_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08944","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1711.08944","created_at":"2026-05-17T23:58:31.098066+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.08944v2","created_at":"2026-05-17T23:58:31.098066+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08944","created_at":"2026-05-17T23:58:31.098066+00:00"},{"alias_kind":"pith_short_12","alias_value":"TLUONH7O7RNI","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TLUONH7O7RNILWAP","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TLUONH7O","created_at":"2026-05-18T12:31:46.661854+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/TLUONH7O7RNILWAPIGVZOJZ2Y5","json":"https://pith.science/pith/TLUONH7O7RNILWAPIGVZOJZ2Y5.json","graph_json":"https://pith.science/api/pith-number/TLUONH7O7RNILWAPIGVZOJZ2Y5/graph.json","events_json":"https://pith.science/api/pith-number/TLUONH7O7RNILWAPIGVZOJZ2Y5/events.json","paper":"https://pith.science/paper/TLUONH7O"},"agent_actions":{"view_html":"https://pith.science/pith/TLUONH7O7RNILWAPIGVZOJZ2Y5","download_json":"https://pith.science/pith/TLUONH7O7RNILWAPIGVZOJZ2Y5.json","view_paper":"https://pith.science/paper/TLUONH7O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.08944&json=true","fetch_graph":"https://pith.science/api/pith-number/TLUONH7O7RNILWAPIGVZOJZ2Y5/graph.json","fetch_events":"https://pith.science/api/pith-number/TLUONH7O7RNILWAPIGVZOJZ2Y5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TLUONH7O7RNILWAPIGVZOJZ2Y5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TLUONH7O7RNILWAPIGVZOJZ2Y5/action/storage_attestation","attest_author":"https://pith.science/pith/TLUONH7O7RNILWAPIGVZOJZ2Y5/action/author_attestation","sign_citation":"https://pith.science/pith/TLUONH7O7RNILWAPIGVZOJZ2Y5/action/citation_signature","submit_replication":"https://pith.science/pith/TLUONH7O7RNILWAPIGVZOJZ2Y5/action/replication_record"}},"created_at":"2026-05-17T23:58:31.098066+00:00","updated_at":"2026-05-17T23:58:31.098066+00:00"}