Journal ArticleDOI
On the use of Petri nets for the enumeration of all trees in a graph
TLDR
A technique utilizing the reachability concept of Petri nets for the enumeration of all the trees in a graph using only vector additions on a single matrix alleviates the computational effort.About:
This article is published in Reliability Engineering.The article was published on 1984-01-01. It has received 9 citations till now. The article focuses on the topics: Petri net & Graph (abstract data type).read more
Citations
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Journal ArticleDOI
A petri net approach to determine all spanning trees for overall reliability analysis of general networks
Vinod Kumar,K. K. Aggarwal +1 more
TL;DR: The reachability, marking and firing concepts of PNs are exploited to enumerate all spanning trees of a network by assigning meaningful interpretation to the entities of the PN.
Journal ArticleDOI
Determination of all hamiltonian paths and circuits and the minimal feedback set in a graph through Petri nets
TL;DR: The proposed technique for the determination of all Hamiltonian paths and all circuits requires only vector additions on the columns of a single matrix as compared to the matrix multiplications required in the existing techniques, alleviating the computational efforts.
Book ChapterDOI
CHAPTER 9 - Use of Petri Nets for System Reliability Evaluation
TL;DR: This chapter provides an introduction of Petri nets, their modeling capabilities, techniques of analysis and a brief discussion on several extended Petrinets.
Journal ArticleDOI
An improved method of enumerating all trees and minimal paths in a graph using Petri nets
J.M. Kontoleon,D. Mandaltsis +1 more
TL;DR: Two algorithms based on the concept of reachability in Petri nets are presented, which always enumerate only real trees and minimal paths while similar earlier techniques sometimes fail at this point.
References
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Journal ArticleDOI
State equation, controllability, and maximal matchings of petri nets
TL;DR: This paper discusses Petri nets in the context of the state equation for a linear discrete-time system and shows that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.
Journal ArticleDOI
Generation of Trees without Duplications
W. Mayeda,S. Seshu +1 more
TL;DR: A practical procedure satisfying these conditions is presented and it is shown that for practical networks the number of trees exceeds the fast memory of any computer and, hence, slows down search for duplicates.
Journal ArticleDOI
A petri net approach to enumerate all system success paths for reliability evaluation of a complex system
TL;DR: A Petri net approach to enumerate all system success paths between a specified pair of nodes that requires only vector additions on a single matrix is presented.
Journal ArticleDOI
A Method of Tree Expansion in Network Topology
TL;DR: This paper presents a systematic method of obtaining the total sum of all possible tree admittance products of a very complicated network that is partitioned into several simple subnetworks by a set of independent cut sets.
Journal ArticleDOI
Enumeration of all trees of a graph
TL;DR: In this paper, the nonsingular submatrices of the characteristic part of the fundamental cutset matrix relative to a tree uniquely correspond to the other trees of a graph G. Using this principle, a method of listing, without duplication, all trees of G is presented.