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If gamma(v)=c, for all v in V, then the gamma-L-flow is called a c-sum L-flow. In this paper we study the existence of gamma-L-flows for various choices of sets L of real numbers, with an emphasis on 1-sum flows.\n  Given a natural k number, a c-sum k-flow is a c-sum flow with values from the set "},"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":"1503.07131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-24T18:30:28Z","cross_cats_sorted":[],"title_canon_sha256":"98ac00c49589f6ced9dff781baf988886ff1bc31a52804235e950411b4df12d3","abstract_canon_sha256":"bb1b5ba692e06d927982437f299dda63446172f99b05ecd472da6357c8a68c0c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:29.342830Z","signature_b64":"C+pKiUwKh72T/fpFwGoPsWvOLrQUl1u++ZMZsc6A3s4FtzZz2PTvMqleFsoGaXXXMV0ZZVBL57fCghu+e7MmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91fe1abc04f5bcd8ef8aee171f5fe85847e264710f6ba71da37a38b7648a3e59","last_reissued_at":"2026-05-18T02:20:29.342243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:29.342243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On 1-sum flows in undirected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"K. 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