【摘要】 本文对顶点权的含意作了推广:一个图的顶点权不仅能表示该顶点‘自身’的权,也可以代表一个片断图、一个含有同谱点的片断、两个具有等价点的同谱片断收缩的结果.对两点之间的桥也作了同样推广.本文依据收缩定理和同谱定理讨论了同谱点和无约束点的性质,并给予必要的数学证明.还从几个简单图出发,利用上述性质,导出了一系列同谱图.更多还原

【Abstract】 In present paper, the meaning of vertex weight is extended in a simple HMO calculation. The weight of the vertex in a graph can not only represent the weight of the isolated vertex "itself", but also stand for a deletion of a species with isospectral points or the result of a deletion of two equivalent points in a pair of isospectral graphs. The meaning of the bridge across two vertices is also extended in the same way. On the basis of theories of deletion and isospectrum the properties of the isospectral points and unrestricted points are discussed in detail and a necessary proof is given by our mathematical approach. Some isospectral mates and method for constructing isospectral graphs which have been reported in literature can be easily obtained by applying these properties. A series of complex isospectral pairs are derived from some simple graphs using the foregoing properties.更多还原