Saturation number of nanotubes - Tratnik, Niko (Ars mathematica contemporanea, 2017)
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 ?${\rm C_4C_6}$?-tubes. Further, upper and lower bounds for the saturation number of armchair, zig-zag, ?${\rm TUC_4C_8(S)}$? and ?${\rm TUC_4C_8(R)}$? nanotubes are calculated.
Keywords: cevček; cik-cak nanocevčica; maksimalno prirejanje; nanocevka naslanjač; nasičenostno število; povezavno dominacijsko število; sklenjena benzenoidna veriga; učinkovita povezavna dominacijska množica