模糊图的g-割点和g-割边的性质

Properties of g-cut Vertices and g-cut Edges of Fuzzy Graphs

模糊图理论是一门建立在模糊集理论与经典图论基础上的模糊数学分支,其目的是为系统工程、网络设计、计算机科学等领域中的不确定性信息提供分析模型。本文首先引入了模糊图的g-割点和g-割边的概念,其次研究了模糊树、完全模糊图、模糊圈的g-割点和g-割边的相关性质,最后讨论了其在通信网络方面的应用。本文的研究为寻找通信网络中关键设备及线路提供理论依据,有利于更精确地检测和维护通信系统的稳定性。

Fuzzy graph theory is a branch of fuzzy mathematics,which is based on fuzzy set theory and classical graph theory.It aims to provide analytical models for uncertain information in the fields such as system engineering,network design,and computer science.This paper first introduces the concept of g-cut vertices and g-cut edges of fuzzy graphs,then investigates the related properties of g-cut vertices and g-cut edges of fuzzy trees,complete fuzzy graphs and fuzzy cycles,and finally discusses their applications in communication networks.The research in this paper provides a theoretical basis for finding key devices and links in communication networks,which is useful for detecting and maintaining the stability of communication systems more accurately.