On graphs with perfect internal matchings

  Miklós Bartha Éva Gombás

Abstract:

  Graphs with perfect internal matchings are studied as underlying objects of certain molecular switching devices called soliton automata. A perfect internal matching of a graph is a matching that covers all vertices of the graph, except possibly those with degree one. Such a matching is called a state of the graph. It is proved that for every two states there exists a so called mediator alternating network which can be used as a switch between those two states. As a consequence of this result it is shown how transitions of soliton automata can be decomposed into a sequence of simpler moves. Elementary graphs having a perfect internal matching are defined through an equivalence relation on their edges. Another equivalence relation on the set of vertices is introduced to characterize the well-known canonical partition of elementary graphs in the new generalized sense.

 Gyenizse Pal 1996. Augusztus 29. Csütörtök 09:59:38 MET DST