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A graph $G$ is called a \\emph{group distance magic graph} if there exists a $\\Gamma $-distance magic labeling for every Abelian group $\\Gamma$ of order $|V(G)|$.\n  In this paper we prove that some complete $k$-partite graphs are $\\mathbb{Z}_p$-distance magic. Moreover we prove that $K_{m,n}$ i"},"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":"1302.6131","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-25T15:52:59Z","cross_cats_sorted":[],"title_canon_sha256":"7246b9e562684c1bb7b1ce51979c85818a113b3ab838a8000f5f8ef843beb56d","abstract_canon_sha256":"730c8126e60914eb6fc72e4932129c9803cb539eee557f424af8caec4308e266"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:11.193262Z","signature_b64":"KneB1an/YAevpOivgMnTMIpY0H3PDa/APbkvMlXPv+1m8OTTFnjwaLA2WAz5Jh0VP6fYulBbqC30i52rRnPdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33e535f8ebe2a0a6466f92512d7420a06b2d1c0be5141435a6bdc1eedbd8ff1e","last_reissued_at":"2026-05-18T00:29:11.192682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:11.192682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Note on group distance magic complete bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sylwia Cichacz","submitted_at":"2013-02-25T15:52:59Z","abstract_excerpt":"A $\\Gamma$-distance magic labeling of a graph $G=(V,E)$ with $|V | = n$ is a bijection $\\ell$ from $V$ to an Abelian group $\\Gamma$ of order $n$ such that the weight $w(x)=\\sum_{y\\in N_G(x)}\\ell(y)$ of every vertex $x \\in V$ is equal to the same element $\\mu \\in \\Gamma$, called the \\emph{magic constant}. A graph $G$ is called a \\emph{group distance magic graph} if there exists a $\\Gamma $-distance magic labeling for every Abelian group $\\Gamma$ of order $|V(G)|$.\n  In this paper we prove that some complete $k$-partite graphs are $\\mathbb{Z}_p$-distance magic. 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