Saturation number of nanotubes
Keywords:Saturation number, maximal matching, edge domination number, efficient edge dominating set, closed benzenoid chain, armchair nanotube, zig-zag nanotube, tubulene, TUC_4C_8(S) nanotube, TUC_4C_8(R) nanotube
In the present paper we are interested in the saturation number of closed benzenoid chains and certain families of nanotubes. The saturation number of a graph is the cardinality of a smallest maximal matching in the graph. The problem of determining the saturation number is related to the edge dominating sets and efficient edge dominating sets in a graph. We establish the saturation number of some closed benzenoid chains and C4C6-tubes. Further, upper and lower bounds for the saturation number of armchair, zig-zag, TUC4C8(S) and TUC4C8(R) nanotubes are calculated.