Complete forcing numbers of hexagonal systems

As a strengthening of the concept global forcing number graph G, complete G is cardinality minimum edge subset to which restriction every perfect matching M set M. Xu et al. (J Comb Opt 29: 803–814, 2015) revealed that also antifores each matching, and obtained for catacondensed hexagonal system, equal Clar plus hexagons (Chan MATCH Commun Math Comput Chem 74: 201–216, 2015). In this paper, we consider general systems H, present sharp upper bound on H in terms elementary edge-cut cover lower via decomposition as well. Through such approaches, obtain some closed formulas numbers types including parallelogram, regular hexagon- rectangle-shaped systems.