{"paper":{"title":"On Symmetry of Independence Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Eugen Mandrescu, Vadim E. Levit","submitted_at":"2011-05-11T14:22:17Z","abstract_excerpt":"An independent set in a graph is a set of pairwise non-adjacent vertices, and alpha(G) is the size of a maximum independent set in the graph G. A matching is a set of non-incident edges, while mu(G) is the cardinality of a maximum matching.\n  If s_{k} is the number of independent sets of cardinality k in G, then I(G;x)=s_{0}+s_{1}x+s_{2}x^{2}+...+s_{\\alpha(G)}x^{\\alpha(G)} is called the independence polynomial of G (Gutman and Harary, 1983). If $s_{j}=s_{\\alpha-j}$, 0=< j =< alpha(G), then I(G;x) is called symmetric (or palindromic). It is known that the graph G*2K_{1} obtained by joining each"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2202","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"}