Saturation number of nanotubes

Niko Tratnik, Petra Žigert Pleteršek

Abstract


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.


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

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ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications