Marked graphs and hamiltonian graphs
In this paper we present an algorithm using a sign incidence matrix to enumerate all the subsets of places of a marked graph which are both siphon and trap, whose input transitions equal the output transitions and where both of them equal the set of all transitions. An iterative procedure to find a set of places in a marked graph whose removal ensures the resulting marked graph does not have a subset of places which are both siphon and trap, is given. This iterative procedure employs a siphon-trap matrix. As an application, using the algorithm given earlier, we have obtained all Hamiltonian circuits of a given directed graph. We have also found the minimal feedback edge set of a given directed graph. A characterization for Hamiltonian graphs is obtained in terms of siphons and traps.