In this paper, as a natural extension of the Rényi formula which counts labeled connected unicyclic graphs, we present a formula for the number of labeled（k ＋ 1）-uniform（p, q）-unicycles as follows：U（k＋1）...In this paper, as a natural extension of the Rényi formula which counts labeled connected unicyclic graphs, we present a formula for the number of labeled（k ＋ 1）-uniform（p, q）-unicycles as follows：U（k＋1）p, q={p!/2[（k-1）!]^q·∑t=2q（q^（q-t-1）· sgn（tk- 2））/（q- t）!, p = qk,0, p≠qk,where k, p, q are positive integers.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11501139)
文摘In this paper, as a natural extension of the Rényi formula which counts labeled connected unicyclic graphs, we present a formula for the number of labeled（k ＋ 1）-uniform（p, q）-unicycles as follows：U（k＋1）p, q={p!/2[（k-1）!]^q·∑t=2q（q^（q-t-1）· sgn（tk- 2））/（q- t）!, p = qk,0, p≠qk,where k, p, q are positive integers.
