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J4 ›› 2013, Vol. 48 ›› Issue (6): 104-110.

• 论文 • 上一篇    

模糊图的乘积运算及相关分解

王东燕,李生刚*,杨文华   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710062
  • 收稿日期:2013-01-17 出版日期:2013-06-20 发布日期:2013-06-09
  • 通讯作者: 李生刚(1959-),男,教授,研究方向为格上拓扑学与图论.Email: shenggangli@yahoo.com.cn
  • 作者简介:王东燕(1985- ),女,硕士研究生,研究方向为图论.Email: wangdongyan10@yahoo.cn
  • 基金资助:

    国家自然科学基金资助项目(11071151);陕西省自然科学基金资助项目(2010JM1005)

The product operations and related decompostions of fuzzy graphs

WANG Dong-yan, LI Shenggang*, YANG Wen-hua   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China
  • Received:2013-01-17 Online:2013-06-20 Published:2013-06-09

摘要:

定义了两个模糊图的字典乘积并给出了一个模糊图能分解成两个模糊图的强乘积、直接乘积、字典乘积的充分条件或必要条件。 证明了两个模糊图的偏模糊子图的强乘积、直接乘积、字典乘积是这两个模糊图的强乘积、直接乘积、字典乘积的偏模糊子图。 最后给出了与这三种乘积运算相关的同构定理。

关键词: 模糊图;分解;笛卡尔乘积;强乘积;直接乘积;字典乘积;同构

Abstract:

The lexicographic product of two fuzzy graphs and gives some necessary or sufficient conditions are given under which a fuzzy graph can be decomposited into a strong product, direct and lexicographic product of two fuzzy graphs. It is proved that the strong product, direct product or lexicographic product of partial fuzzy subgraphs of two fuzzy graphs is a partial fuzzy subgraph of strong product, direct product or lexicographic product of the two fuzzy graphs. Some isomorphism theorems on these products of fuzzy graphs are also obtained.

Key words: fuzzy graph; decomposition; cartesian product; strong product; direct product; lexicographic product; isomorphism

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