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.

DOI: 10.1504/IJSEM.2012.048622

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 *

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