{"paper":{"title":"Eigenvalues of a H-generalized join graph operation constrained by vertex subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Domingos M. Cardoso, Enide A. Martins, Maria Robbiano, Oscar Rojo","submitted_at":"2012-05-08T17:28:09Z","abstract_excerpt":"Considering a graph $H$ of order $p$, a generalized $H$-join operation of a family of graphs $G_1,..., G_p$, constrained by a family of vertex subsets $S_i \\subseteq V(G_i)$, $i=1,..., p,$ is introduced. When each vertex subset $S_i$ is $(k_i,\\tau_i)$-regular, it is deduced that all non-main adjacency eigenvalues of $G_i$, different from $k_i-\\tau_i$, for $i=1,..., p,$ remain as eigenvalues of the graph $G$ obtained by the above mentioned operation. Furthermore, if each graph $G_i$ of the family is $k_i$-regular, for $i=1,..., p$, and all the vertex subsets are such that $S_i=V(G_i)$, the $H$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1752","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"}