Application of Edge-chain Matrices of Graph to find all Eulerian Cycles
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DOI: 10.23977/meimie.2019.43072
Author(s)
Zunhai Gao, Zhuo Chen
Corresponding Author
Zunhai Gao
ABSTRACT
The initial edge-chain matrix and general edge-chain matrix of graph are presented. The operations of the general edge-chain matrices are derived, by which a method to find all Eulerian cycles is obtained. Only through some power operations of the initial edge-chain matrix, can reveal all Eulerianian cycles which are showed in the final edge-chain matrix. This method can determine whether Eulerianian cycles exist or not and if they do can also find out all of them. It is effective to directed or undirected finite graph. And it can be simplified by computations of some row vectors and column vectors of some power of the initial edge-matrix. This pure mathematical method shows the results more intuitive and makes program operation easier.
KEYWORDS
Graph, edge-chain matrix, multiplication of edge-chain matrix, Eulerianian path, Eulerianian cycle)