{"paper":{"title":"Completely Positive formulation of the Graph Isomorphism Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Pawan Aurora, Shashank K Mehta","submitted_at":"2013-01-11T05:30:45Z","abstract_excerpt":"Given two graphs $G_1$ and $G_2$ on $n$ vertices each, we define a graph $G$ on vertex set $V_1\\times V_2$ and the edge set as the union of edges of $G_1\\times \\bar{G_2}$, $\\bar{G_1}\\times G_2$, $\\{(v,u'),(v,u\"))(|u',u\"\\in V_2\\}$ for each $v\\in V_1$, and $\\{((u',v),(u\",v))|u',u\"\\in V_1\\}$ for each $v\\in V_2$. We consider the completely-positive Lov\\'asz $\\vartheta$ function, i.e., $cp\\vartheta$ function for $G$. We show that the function evaluates to $n$ whenever $G_1$ and $G_2$ are isomorphic and to less than $n-1/(4n^4)$ when non-isomorphic. Hence this function provides a test for graph isom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2390","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"}