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In this article, we characterize the enhanced power graph $\\mathcal{G}_e(G)$ of $G$. The graph $\\mathcal{G}_e(G)$ is complete if and only if $G$ is cyclic, and $\\mathcal{G}_e(G)$ is Eulerian if and only if $|G|$ is odd. We classify all abelian groups and also all non-abelian $p-$groups $G$ for which $\\mathcal{G}_e(G)$ s"},"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":"1606.03209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-10T06:53:31Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"08205211bf0a1cee14642cf61324928606c66e7595409df8b0274f0cb6683797","abstract_canon_sha256":"262ea91454f2484570b9a0c13d551e0b0792b7b9ffc60eb25b770bdf28842f0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:58.792643Z","signature_b64":"yNOux3eLc+F7bF8lbHdOlGQnNZQXj+2GUHg6SJkPjzgjAr+73u4FxaXGLe+WY0YUDNguS8+Jsxnmup6nRV/kAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"457616d244015e7ccf926df5d90e088fceac248727d214a854428112f2bc0b12","last_reissued_at":"2026-05-18T01:11:58.792242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:58.792242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some properties of enhanced power graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"A. K. Bhuniya, Sudip Bera","submitted_at":"2016-06-10T06:53:31Z","abstract_excerpt":"Given a group $G$, the enhanced power graph of $G$ denoted by $\\mathcal{G}_e(G)$, is the graph with vertex set $G$ and two distinct vertices $x, y$ are edge connected in $\\mathcal{G}_e(G)$ if there exists $z\\in G $ such that $x=z^m$ and $ y=z^n $, for some $m, n\\in \\mathbb{N}$. In this article, we characterize the enhanced power graph $\\mathcal{G}_e(G)$ of $G$. The graph $\\mathcal{G}_e(G)$ is complete if and only if $G$ is cyclic, and $\\mathcal{G}_e(G)$ is Eulerian if and only if $|G|$ is odd. We classify all abelian groups and also all non-abelian $p-$groups $G$ for which $\\mathcal{G}_e(G)$ s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03209","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":"1606.03209","created_at":"2026-05-18T01:11:58.792302+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.03209v1","created_at":"2026-05-18T01:11:58.792302+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03209","created_at":"2026-05-18T01:11:58.792302+00:00"},{"alias_kind":"pith_short_12","alias_value":"IV3BNUSEAFPH","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IV3BNUSEAFPHZT4S","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IV3BNUSE","created_at":"2026-05-18T12:30:22.444734+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/IV3BNUSEAFPHZT4SNX25SDQIR7","json":"https://pith.science/pith/IV3BNUSEAFPHZT4SNX25SDQIR7.json","graph_json":"https://pith.science/api/pith-number/IV3BNUSEAFPHZT4SNX25SDQIR7/graph.json","events_json":"https://pith.science/api/pith-number/IV3BNUSEAFPHZT4SNX25SDQIR7/events.json","paper":"https://pith.science/paper/IV3BNUSE"},"agent_actions":{"view_html":"https://pith.science/pith/IV3BNUSEAFPHZT4SNX25SDQIR7","download_json":"https://pith.science/pith/IV3BNUSEAFPHZT4SNX25SDQIR7.json","view_paper":"https://pith.science/paper/IV3BNUSE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.03209&json=true","fetch_graph":"https://pith.science/api/pith-number/IV3BNUSEAFPHZT4SNX25SDQIR7/graph.json","fetch_events":"https://pith.science/api/pith-number/IV3BNUSEAFPHZT4SNX25SDQIR7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IV3BNUSEAFPHZT4SNX25SDQIR7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IV3BNUSEAFPHZT4SNX25SDQIR7/action/storage_attestation","attest_author":"https://pith.science/pith/IV3BNUSEAFPHZT4SNX25SDQIR7/action/author_attestation","sign_citation":"https://pith.science/pith/IV3BNUSEAFPHZT4SNX25SDQIR7/action/citation_signature","submit_replication":"https://pith.science/pith/IV3BNUSEAFPHZT4SNX25SDQIR7/action/replication_record"}},"created_at":"2026-05-18T01:11:58.792302+00:00","updated_at":"2026-05-18T01:11:58.792302+00:00"}