网络最短的最优解集结构

数学季刊 ›› 2007, Vol. 22 ›› Issue (4): 530-537.

网络最短的最优解集结构

1.Department of Scientific Research Affairs,Hnanghuai University,Zhumadian 463000,China;2.Basic Science Institute,Zhongzhou University,Zhengzhou 450052,China

收稿日期:2004-11-10 出版日期:2007-12-30 发布日期:2023-10-20
作者简介:ZHANG Zhen-kun(1971-), male, native of Runan, Henan, an associate professor of Huanghuai University, Ph.D., engages in graph theory and combinatorial optimization.

The Structure of the Optimal Solution Set on the Shortest Paths for Networks

1.Department of Scientific Research Affairs,Hnanghuai University,Zhumadian 463000,China;2.Basic Science Institute,Zhongzhou University,Zhengzhou 450052,China

Received:2004-11-10 Online:2007-12-30 Published:2023-10-20
About author:ZHANG Zhen-kun(1971-), male, native of Runan, Henan, an associate professor of Huanghuai University, Ph.D., engages in graph theory and combinatorial optimization.

摘要/Abstract

摘要： The shortest path problem in a network G is to find shortest paths between some specified source vertices and terminal vertices when the lengths of edges are given. The structure of the optimal solutions set on the shortest paths is studied in this paper. First,the conditions of having unique shortest path between two distinguished vertices s and t in a network G are discussed;Second,the structural properties of 2-transformation graph G on the shortest-paths for G are presented heavily.

关键词: networks, the shortest-paths, 2-transformation graphs, structural properties

Abstract: The shortest path problem in a network G is to find shortest paths between some specified source vertices and terminal vertices when the lengths of edges are given. The structure of the optimal solutions set on the shortest paths is studied in this paper. First,the conditions of having unique shortest path between two distinguished vertices s and t in a network G are discussed;Second,the structural properties of 2-transformation graph G on the shortest-paths for G are presented heavily.

Key words: networks, the shortest-paths, 2-transformation graphs, structural properties

中图分类号:

TN915

张振坤, 王斌. 网络最短的最优解集结构[J]. 数学季刊, 2007, 22(4): 530-537.

ZHANG Zhen-kun, WANG Bina. The Structure of the Optimal Solution Set on the Shortest Paths for Networks[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(4): 530-537.

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