Weighted directed graph: a Petri net-based method of extraction of closed weighted directed Euler trail

This paper investigates the closed weighted directed Euler trail using sign incidence matrix and siphon-trap matrix of Petri net (PN) model of weighted directed graph. We obtain all set of places those are siphon as well as trap using the siphon-trap and bounded-ness property of PN, by operating Boolean addition on elements of columns in sign incidence matrix representation of PN model. The union of such all set of places will constitutes a partition of the edge set of the original graph. Then edges corresponding to these places will forms a closed weighted Euler trail, which ensure that graph is Eulerian graph.