This paper is concerned with the enumeration of a special kind of labeled connected graphs of which the cutpoint-graphs are trees.A new method—treelization is introduced, by which the enumeration of this special kind...This paper is concerned with the enumeration of a special kind of labeled connected graphs of which the cutpoint-graphs are trees.A new method—treelization is introduced, by which the enumeration of this special kind of graphs can be solved. The enumerative formula with generating function is derived. The method of treelization is powerful in solving enumeration problems of graphs and deserves further research. For example, using the similar way, another special kind of labeled connected graphs of which the block-graphs are trees can be enumerated.展开更多
证明了体积增长不低于5次多项式的拟顶点可迁图上的简单随机游走几乎处处有无穷多个切割时,从而有无穷多个切割点.该结论在所论情形下肯定了Benjamini,Gurel-Gurevich和Schramm在文[2011,Cutpoints and resistance of random walk paths...证明了体积增长不低于5次多项式的拟顶点可迁图上的简单随机游走几乎处处有无穷多个切割时,从而有无穷多个切割点.该结论在所论情形下肯定了Benjamini,Gurel-Gurevich和Schramm在文[2011,Cutpoints and resistance of random walk paths,Ann.Probab.,39(3):1122-1136]中提出的猜想:顶点可迁图上暂留简单随机游走几乎处处有无穷多个切割点.展开更多
文摘This paper is concerned with the enumeration of a special kind of labeled connected graphs of which the cutpoint-graphs are trees.A new method—treelization is introduced, by which the enumeration of this special kind of graphs can be solved. The enumerative formula with generating function is derived. The method of treelization is powerful in solving enumeration problems of graphs and deserves further research. For example, using the similar way, another special kind of labeled connected graphs of which the block-graphs are trees can be enumerated.
文摘证明了体积增长不低于5次多项式的拟顶点可迁图上的简单随机游走几乎处处有无穷多个切割时,从而有无穷多个切割点.该结论在所论情形下肯定了Benjamini,Gurel-Gurevich和Schramm在文[2011,Cutpoints and resistance of random walk paths,Ann.Probab.,39(3):1122-1136]中提出的猜想:顶点可迁图上暂留简单随机游走几乎处处有无穷多个切割点.
