2011/04/23 by Rashid Zaare-Nahandi, Zaare-Nahandi, Rashid
Mathematics · #05C25 #05E40 #05E45 #13F55 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:05C25 #msc:05E40 #msc:05E45 #msc:13F55
paper · pdf · doi:10.48550/arxiv.1104.4556
10 pages. arXiv admin note: substantial text overlap with arXiv:1009.5242
arxiv created 2012/07/10 · arxiv updated 2012/07/11
A graph G is called well-covered if all maximal independent sets of vertices have the same cardinality. A simplicial complex Δ is called pure if all of its facets have the same cardinality. Let \mathcal G be the class of graphs with some disjoint maximal cliques covering all vertices. In this paper, we prove that for any simplicial complex or any graph, there is a corresponding graph in class \mathcal G with the same well-coveredness property. Then some necessary and sufficient conditions are presented to recognize fast when a graph in the class \cal G is well-covered or not. To do this characterization, we use an algebraic interpretation according to zero-divisor elements of the edge rings of graphs.