Intuitionistic Fuzzy Cycles and Intuitionistic Fuzzy Trees

Muhammad Akram,N O Alshehri

doi:10.1155/2014/305836

Muhammad Akram, N O Alshehri

Open Access

https://doi.org/10.1155/2014/305836

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Abstract

Connectivity has an important role in neural networks, computer network, and clustering. In the design of a network, it is important to analyze connections by the levels. The structural properties of intuitionistic fuzzy graphs provide a tool that allows for the solution of operations research problems. In this paper, we introduce various types of intuitionistic fuzzy bridges, intuitionistic fuzzy cut vertices, intuitionistic fuzzy cycles, and intuitionistic fuzzy trees in intuitionistic fuzzy graphs and investigate some of their interesting properties. Most of these various types are defined in terms of levels. We also describe comparison of these types.

Highlights

A graph theory has many applications in different areas of computer science including data mining, image segmentation, clustering, image capturing, and networking
Fuzzy graph theory is finding an increasing number of applications in modeling real time systems where the level of information inherent in the system varies with different levels of precision
Fuzzy models are becoming useful because of their aim in reducing the differences between the traditional numerical models used in engineering and sciences and the symbolic models used in expert systems

Summary

Introduction

A graph theory has many applications in different areas of computer science including data mining, image segmentation, clustering, image capturing, and networking. The concepts of paths, walks, and circuits in graph theory are used in traveling salesman problem, database design concepts, and resource networking. This leads to the development of new algorithms and new theorems that can be used in tremendous applications. Rosenfeld [4] introduced the fuzzy analogue of several basic graph-theoretic concepts including bridges, cut nodes, connectedness, trees, and cycles. We introduce various types of intuitionistic fuzzy bridges, intuitionistic fuzzy cut vertices, intuitionistic fuzzy cycles, and intuitionistic fuzzy trees in intuitionistic fuzzy graphs and investigate some of their interesting properties. Terminologies, and applications not mentioned in the paper, the readers should refer to [3, 5, 7, 8, 10, 16,17,18,19,20,21,22,23]

Preliminaries

Cycles and Trees

Conclusions