match Communications in Mathematical and in Computer Chemistry · 2021 · 11 citations · 14 references
Natural SciencesComputer ScienceMathematicsAlgorithmsCombinatoricsOptimizationAlgebraic CombinatoricsCombinatorial OptimizationEnumerative CombinatoricsGraph AlgorithmsInteger ProgrammingLinear ProgrammingEnumeration Algorithms For GraphsEnumerative AlgorithmsGraph EnumerationGraph MatchingInteger Linear ProgrammingMatching AlgorithmsMatching ProblemsMatchings Enumeration
The forcing polynomial and anti-forcing polynomial are two important enumerative polynomials associated with all perfect matchings of a graph. In a graph with large order, the exhaustive enumeration which is used to compute forcing number of a given perfect matching is too time-consuming to compute anti-forcing number. In this paper, we come up with an efficient method — integer linear programming, to compute forcing number and anti-forcing number of a given perfect matching. As applications, we obtain the di-forcing polynomials C60 , C70 and C72 , and as a consequence, the forcing and anti-forcing polynomials of them are obtained.
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Resonance in C60 buckminsterfullerene
Douglas J. Klein, Thomas Schmalz, G. E. Hite et al. · Journal of the American Chemical Society · 1986 · 207 citations