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A criterion is specified for identifying graphs with non-empty critical independent sets. A polynomial-time algorithm is given for finding them and, thus, reducing the problem of finding a maximum independent set (MIS) in such a graph to finding a MIS in a proper subgraph. This algorithm can be extended to identify maximum cardinality critical independent(More)
The independence number of the graph of a fullerene, the size of the largest set of vertices such that no two are adjacent (corresponding to the largest set of atoms of the molecule, no pair of which are bonded), appears to be a useful selector in identifying stable fullerene isomers. The experimentally characterized isomers with 60, 70 and 76 atoms(More)
The annihilation number a of a graph is an upper bound of the independence number α of a graph. In this article we characterize graphs with equal independence and annihilation numbers. In particular, we show that α = a if, and only if, either (1) a ≥ n 2 and α ′ = a, or (2) a < n 2 and there is a vertex v ∈ V (G) such that α ′ (G − v) = a(G), where α ′ is(More)
Abnormal electroencephalographic seizure-like activity and myoclonic movements have been recognized during enflurane anesthesia. This is most commonly seen in the presence of respiratory alkalosis and high concentrations of enflurane. Immediate and delayed postoperative generalized tonic-clonic convulsions have also been reported after enflurane anesthesia.(More)
Given a connected bipartite graph G, we describe a procedure which enumerates and computes all graphs H (if any) for which there is a direct product factorization G ∼ = H × K 2. We apply this technique to the problems of factoring even cycles and hypercubes over the direct product. In the case of hypercubes, our work expands some known results by Brešar,(More)
Every connected graph G with radius r(G) and independence number α(G) obeys α(G) ≥ r(G). Recently the graphs for which equality holds have been classified. Here we investigate the members of this class that are Cartesian products. We show that for non-trivial graphs G and H, α(G2H) = r(G2H) if and only if one factor is a complete graph on two vertices, and(More)
In a classical 1986 paper by Erdös, Saks and Sós every graph of radius r has an induced path of order at least 2r − 1. This result implies that the independence number of such graphs is at least r. In this paper, we use a result of S. Fajtlowicz about radius-critical graphs to characterize graphs where the independence number is equal to the radius, for all(More)