{"paper":{"title":"The Sierpi\\'nski product of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arjana \\v{Z}itnik, Jurij Kovi\\v{c}, Sara Sabrina Zemlji\\v{c}, Toma\\v{z} Pisanski","submitted_at":"2019-04-08T16:37:24Z","abstract_excerpt":"In this paper we introduce a product-like operation that generalizes the construction of generalized Sierpi\\'nski graphs. Let $G,H$ be graphs and let $f: V(G) \\to V(H)$ be a function. Then the Sierpi\\'nski product of $G$ and $H$ with respect to $f$ is defined as a pair $(K,\\varphi)$, where $K$ is a graph on the vertex set $V(G) \\times V(H)$ with two types of edges:\n  -- $\\{(g,h),(g,h')\\}$ is an edge in $K$ for every $g\\in V(G)$ and every $\\{h,h'\\}\\in E(H)$,\n  -- $\\{(g,f(g'),(g',f(g))\\}$ is an edge in $K$ for every edge $\\{g,g'\\} \\in E(G)$; and $\\varphi: V(G) \\to V(K)$ is a function that maps e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04180","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"}