无向循环图与广义de@Bruijn有向图的支撑树与欧拉环游的计数

本文首先讨论度数为奇数的无向循环图的支撑树问题，给出其解析表达式及渐近结果，并给出一有效方法来计算支撑树数目。接着，本文还讨论了广义deBruijn有向图的情况，特别给出一类特殊的广义deBruijn有向图的支撑树与欧拉环游数目的简洁表达式。由于叠线图的支撑树数目与原图的支撑树数目有密切关系，所以这两类图的叠线图的支撑树数目也相应可以得到。At first, this paper discuseed the number of spanning trees in the undirectedcirculant graphs with odd degrees, giving an eppression and an asymptotic result, also providing an eggective method to calculate the numbers. Then, the paper discussed the case of generalized de Bruijn digraphs, eppecially providigan explicit expression on the number of spanning trees and Eulerian trails in a special kin...学位：理学硕士院系专业：数学科学学院_概率论与数理统计学号：19992301

The k-tuple twin domination in generalized de Bruijn and Kautz networks

AbstractGiven a digraph (network) G=(V,A), a vertex u in G is said to out-dominate itself and all vertices v such that the arc (u,v)∈A; similarly, u in-dominates both itself and all vertices w such that the arc (w,u)∈A. A set D of vertices of G is a k-tuple twin dominating set if every vertex of G is out-dominated and in-dominated by at least k vertices in D, respectively. The k-tuple twin domination problem is to determine a minimum k-tuple twin dominating set for a digraph. In this paper we investigate the k-tuple twin domination problem in generalized de Bruijn networks GB(n,d) and generalized Kautz GK(n,d) networks when d divides n. We provide construction methods for constructing minimum k-tuple twin dominating sets in these networks. These results generalize previous results given by Araki [T. Araki, The k-tuple twin domination in de Bruijn and Kautz digraphs, Discrete Mathematics 308 (2008) 6406–6413] for de Bruijn and Kautz networks

Exact sampling with Markov chains

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.Includes bibliographical references (p. 79-83).by David Bruce Wilson.Ph.D

A study on two arc routing problems

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal