Title: Weighted directed graph: a Petri net-based method of extraction of closed weighted directed Euler trail
Authors: Sunita Kumawat
Addresses: Department of Applied Mathematics, Amity School of Engineering and Technology (ASET), Amity University Haryana (AUH), Manesar, Gurgaon, Haryana-122 413, India
Abstract: 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.
Keywords: weighted directed graphs; WDG; directed cycle; Euler graphs; Petri nets; siphon trap matrix; sign incidence matrix.
International Journal of Services, Economics and Management, 2012 Vol.4 No.3, pp.252 - 264
Received: 04 Apr 2012
Accepted: 27 Jun 2012
Published online: 15 Nov 2014 *