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In this paper, explicit expressions for the Kirchhoff index, multiplicative degree-Kirchhoff index and number of spanning trees of $G_n$ are determined, respectively. It is surprising to find that the Kirchhoff (resp. multiplicative degree-Kirchhoff) index of $G_n$ is almost one-sixth of its Wiener (resp. Gutman) index. Moreover, let $\\mathcal{G}^r_n$ be the set of subgraphs obtained from $G_n$ by deleting any $r$ vertical edges of $G_n$, where $0\\leqslant r\\leqslant n$. Explicit formulas for the Kirch"},"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":"1906.04339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-11T01:24:32Z","cross_cats_sorted":[],"title_canon_sha256":"a7c0ae492e02fa3ca8af3db6cbb84f587d8550076e4e619263ed3b0844070c36","abstract_canon_sha256":"533fde2b5d302fa97bb825944379f0a8f66b2726e790370e6cfd566bd9b719f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:39.624208Z","signature_b64":"GT/izqH8V/sTBtqfKMRZo7Vbx3DGV7yuV/aktpwtxE/KqjKc878vELQi+eycsFr+lHDbA7C0jSfio+WpoI9GAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9f99708520ac62e91531d871900fb5405aba5fe035d34f13d81c49af2842779","last_reissued_at":"2026-05-17T23:43:39.623605Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:39.623605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resistance distance-based graph invariants and spanning trees of graphs derived from the strong product of $P_2$ and $C_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jianping Li, Yingui Pan","submitted_at":"2019-06-11T01:24:32Z","abstract_excerpt":"Let $G_n$ be a graph obtained by the strong product of $P_2$ and $C_n$, where $n\\geqslant3$. 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