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It is well known that the so called enhanced hypercube $Q_{n, k}(1\\le k \\le n-1)$ is just the Cayley graph $Cay(Z_{2}^{n},S)$ where $S=\\{e_{1},\\ldots, e_{n},\\epsilon_{k}\\}$. In this paper, we obtain the spectrum of $Q_{n, k}$, from which we give an exact formula of the Kirchhoff index of the enhanced hypercube $Q_{n, k}$. Furthermore, we prove that, for a gi"},"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":"1809.07189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-18T03:23:00Z","cross_cats_sorted":[],"title_canon_sha256":"5102073f6c24c3329631a4b1698251584379bff9e63fc3d6f5d52ef5f11680c5","abstract_canon_sha256":"446c636427d4d2f8ca133642c0009f52bee70e6cdcf6676b173cf01268590553"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:20.466293Z","signature_b64":"ScfciuE/ngw7xlRUgevm4grCgwnssMffUODv0Pzeqxvgyyi+D2b74xCUyi1zB6PM1cfqCPjnocFq4iKyCgSzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9eae910c81e4275432ff8ffb8dc4b5b7f424f410ba886d34a7dd07d062e57ed","last_reissued_at":"2026-05-18T00:05:20.465708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:20.465708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Kirchhoff Index of Enhanced Hypercubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ping Xu, Qiongxiang Huang","submitted_at":"2018-09-18T03:23:00Z","abstract_excerpt":"Let $\\{e_{1},\\ldots,e_{n}\\}$ be the standard basis of abelian group $Z_{2}^{n}$, which can be also viewed as a linear space of dimension $n$ over the Galois filed $F_{2}$, and $\\epsilon_{k}=e_k+e_{k+1}+\\cdots+e_n$ for some $1\\le k\\le n-1$. 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