4正则简单图的一个性质

A Character of 4─Regular Simple Graph

正则简单图具有很强的对称性 ;在许多领域都有广泛的应用 .图与其邻接矩阵之间有着一一对应的关系 .文章深入研究了 4-正则图的邻接矩阵 ,得到了一些重要结论 -经过有限次的行列变换 ,邻接矩阵等价于某些特殊形式的矩阵 ,由该特殊矩阵 ,可以一般地构造另一种特殊矩阵 ,这种特殊矩阵正是 3-正则图的邻接矩阵 ,从而可知 ,每个 4-正则简单图均包含

There is a very strong symmetrical character about simple regular graph, which is extensively used in many fields. There is the relationship between the graph and the adjacency matrix. A research is made on the adjacency matrix of 4-regular simple graph, and some important results are obtained —the adjacency matrix becomes a kind of special matrix through a series of changes of rank and column. From the special matrix, another special matrix that is just the adjacency matrix of 3-regular graph can be generally structured. It is proved that there is 3-regular graph in every simple 4-regular simple graph.