{"paper":{"title":"Connectivity and other invariants of generalized products of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F. A. Muntaner-Batle, S. C. L\\'opez","submitted_at":"2013-05-13T10:19:01Z","abstract_excerpt":"Figueroa-Centeno et al. introduced the following product of digraphs: let $D$ be a digraph and let $\\Gamma$ be a family of digraphs such that $V(F)=V$ for every $F\\in \\Gamma$. Consider any function $h:E(D)\\longrightarrow\\Gamma $. Then the product $D\\otimes_{h} \\Gamma$ is the digraph with vertex set $V(D)\\times V$ and $((a,x),(b,y))\\in E(D\\otimes_h\\Gamma)$ if and only if $(a,b)\\in E(D)$ and $(x,y)\\in E(h (a,b))$.\n  In this paper, we introduce the undirected version of the $\\otimes_h$-product, which is a generalization of the classical direct product of graphs and, motivated by it, we also recov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2729","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"}