摘要
In this paper, as a generalization of the binomial random graph model, we define the model of multigraphs as follows： let G（n; {pk}） be the probability space of all the labelled loopless multigraphs with vertex set V = {v1, v2, ..., vn }, in which the distribution of tvi,vj, the number of the edges between any two vertices vi and vj is P{tvi,vj =k}=Pk, k=0, 1,2,...and they are independent of each other. Denote by Xd = Xd（G）,Yd = Yd（G）, Zd = Zd（G） and Zcd = Zcd（G） the number of vertices of G with degree d, at least d, at most d and between c and d. In this paper, we discuss the distribution of Xd, Yd, Zd and Zcd in the probability space G（n; （Pk））.
In this paper, as a generalization of the binomial random graph model, we define the model of multigraphs as follows： let G（n; {pk}） be the probability space of all the labelled loopless multigraphs with vertex set V = {v1, v2, ..., vn }, in which the distribution of tvi,vj, the number of the edges between any two vertices vi and vj is P{tvi,vj =k}=Pk, k=0, 1,2,...and they are independent of each other. Denote by Xd = Xd（G）,Yd = Yd（G）, Zd = Zd（G） and Zcd = Zcd（G） the number of vertices of G with degree d, at least d, at most d and between c and d. In this paper, we discuss the distribution of Xd, Yd, Zd and Zcd in the probability space G（n; （Pk））.
基金
Supported by National Natural Science Fund of China (Grant Nos. 10831001, 10871046, 10971027)
Science and Technology of Science Fund of Fujian Province (Grant No. A0950059)
Science and Technology Development Fund of Fuzhou University (Grant No. 2009-XQ-27)
