{"paper":{"title":"Subspace Sum Graph of a Vector Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angsuman Das","submitted_at":"2017-02-27T11:43:21Z","abstract_excerpt":"In this paper we introduce a graph structure, called subspace sum graph $\\mathcal{G}(\\mathbb{V})$ on a finite dimensional vector space $\\mathbb{V}$ where the vertex set is the collection of non-trivial proper subspaces of a vector space and two vertices $W_1,W_2$ are adjacent if $W_1 + W_2=\\mathbb{V}$. The diameter, girth, connectivity, maximal independent sets, different variants of domination number, clique number and chromatic number of $\\mathcal{G}(\\mathbb{V})$ are studied. It is shown that two subspace sum graphs are isomorphic if and only if the base vector spaces are isomorphic. Finally"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08245","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"}