有向图的反能量是指有向图的反邻接矩阵的能量.本文利用有向图的运算构造出了几类有向图,它们中的每一个都满足有向图的反能量等于其底图的能量.部分回答了Adiga等人在文[The skew energy of a digraph,Linear Algebra Appl.,2010,432:1...有向图的反能量是指有向图的反邻接矩阵的能量.本文利用有向图的运算构造出了几类有向图,它们中的每一个都满足有向图的反能量等于其底图的能量.部分回答了Adiga等人在文[The skew energy of a digraph,Linear Algebra Appl.,2010,432:1825-1835]中提出的一个公开问题.展开更多
Let G be a simple graph. Define R(G) to be the graph obtained from G by adding a new vertex e* corresponding to each edge e = (a, b) of G and by joining each new vertex e* to the end vertices a and b of the edge e cor...Let G be a simple graph. Define R(G) to be the graph obtained from G by adding a new vertex e* corresponding to each edge e = (a, b) of G and by joining each new vertex e* to the end vertices a and b of the edge e corresponding to it. In this paper, we prove that the number of matchings of R(G) is completely determined by the degree sequence of vertices of G.展开更多
文摘有向图的反能量是指有向图的反邻接矩阵的能量.本文利用有向图的运算构造出了几类有向图,它们中的每一个都满足有向图的反能量等于其底图的能量.部分回答了Adiga等人在文[The skew energy of a digraph,Linear Algebra Appl.,2010,432:1825-1835]中提出的一个公开问题.
文摘Let G be a simple graph. Define R(G) to be the graph obtained from G by adding a new vertex e* corresponding to each edge e = (a, b) of G and by joining each new vertex e* to the end vertices a and b of the edge e corresponding to it. In this paper, we prove that the number of matchings of R(G) is completely determined by the degree sequence of vertices of G.
基金Supported by the National Natural Science Foundation of China(11501050)the Fundamental Research Funds for the Central Universities(310812151003,310812152002)
