{"paper":{"title":"A zero-sum problem on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Wei{\\ss}auer","submitted_at":"2016-10-14T11:13:27Z","abstract_excerpt":"Call a graph $G$ zero-forcing for a finite abelian group $\\mathcal{G}$ if for every $\\ell : V(G) \\to \\mathcal{G}$ there is a connected $A \\subseteq V(G)$ with $\\sum_{a \\in A} \\ell(a) = 0$. The problem we pose here is to characterise the class of zero-forcing graphs. It is shown that a connected graph is zero-forcing for the cyclic group of prime order $p$ if and only if it has at least $p$ vertices. When $|\\mathcal{G}|$ is not prime, however, being zero-forcing is intimately linked to the structure of the graph. We obtain partial solutions for the general case, discuss computational issues and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04407","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"}