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)