• Home
  • Submit Paper
  • Check Paper Status
  • Download Certificate/Paper
  • FAQs
  • Feedback
  • Contact Us
Email: ijraset@gmail.com
IJRASET Logo
Journal Statistics & Approval Details
Recent Published Paper
Our Author's Feedback
 •  ISRA Impact Factor 7.894       •  SJIF Impact Factor: 7.538       •  Hard Copy of Certificates to All Authors       •  DOI by Crossref for all Published Papers       •  Soft Copy of Certificates- Within 04 Hours       •  Authors helpline No: +91-8813907089(Whatsapp)       •  No Publication Fee for Paper Submission       •  Hard Copy of Certificates to all Authors       •  UGC Approved Journal: IJRASET- Click here to Check     
  • About Us
    • About Us
    • Aim & Scope
  • Editorial Board
  • Impact Factor
  • Call For Papers
    • Submit Paper Online
    • Current Issue
    • Special Issue
  • For Authors
    • Instructions for Authors
    • Submit Paper
    • Download Certificates
    • Check Paper Status
    • Paper Format
    • Copyright Form
    • Membership
    • Peer Review
  • Past Issue
    • Monthly Issue
    • Special Issue
  • Pay Fee
    • Indian Authors
    • International Authors
  • Topics
ISSN: 2321-9653
Estd : 2013
IJRASET - Logo
  • Home
  • About Us
    • About Us
    • Aim & Scope
  • Editorial Board
  • Impact Factor
  • Call For Papers
    • Submit Paper Online
    • Current Issue
    • Special Issue
  • For Authors
    • Instructions for Authors
    • Submit Paper
    • Download Certificates
    • Check Paper Status
    • Paper Format
    • Copyright Form
    • Membership
    • Peer Review
  • Past Issue
    • Monthly Issue
    • Special Issue
  • Pay Fee
    • Indian Authors
    • International Authors
  • Topics

Ijraset Journal For Research in Applied Science and Engineering Technology

  • Home / Ijraset
  • On This Page
  • Abstract
  • Introduction
  • Conclusion
  • References
  • Copyright

Characteristics of Fuzzy Petersen Graph and Platonic Graph with Fuzzy Rule

Authors: Suguna. R, Naveen. L

DOI Link: https://doi.org/10.22214/ijraset.2022.40273

Certificate: View Certificate

Abstract

Graph theory is the concepts used to study and model various application in different areas. In this paper, we consider the The Petersen and also the Platonic graph using if-then-rules fuzzy numbers. The results are related to the find the degree of odd vertices and even verticesare same by applying if-then-rules through the paths described by fuzzy numbers.

Introduction

I. INTRODUCTION

The first definition of fuzzy graph was introduced by Kaufmann (1973), based on Zadeh’s fuzzy relations (1971) A more elaborate definition is due to Azriel Rosenfeld who considered fuzzy relation on fuzzy sets and developed the theory of fuzzy graph in 1975.

During the same time Yeh and Bang have also introduced various connectedness concepts in fuzzy graph. Till now fuzzy graphs has been witnessing a tremendous growth and finds applications in many branches of engineering and technology.

Fuzzy systems based on fuzzy if-then rules have been successfully applied to varioustheorems in the field of fuzzy control. Fuzzy Rule based system has high comprehensibility because human users can easily understand the meaning of each fuzzy if-then rule through its linguistic interpretation. Graph theory has numerous applications to problems in system analysis, operation research, transportation and economics. In many cases, however some aspects of graph theoretic problem may be uncertain. For example, the vehicle travel time or vehicle capacity on a road network may not be known exactly. In such cases, it is natural to deal with the uncertainly using fuzzy set theory. The concepts of a fuzzy graph are a natural generalization of crisp graphs, given by Rosenfeld [Zadeh et al., 1975] .

II. BASIC CONCEPT

A. Definition 2.1

A graph G consists of a pair G: (V,E) where V(G) is a non empty finite set whose elements are called points or vertices and E(G) is a set of unordered pairs of distinct elements of V(G). The elements of E(G) are called lines or edges of the graph G.

III. FUZZY PETERSEN GRAPH WITH FUZZY RULE

Conclusion

In this paper we obtain that petersen graph and platonic graph . We conclude that the odd degree of vertices is equal to the even degree of vertices, for both the above cases with the help of IF-THEN rules (i.e., L.H.S=R.H.S).Finally, IF-THEN rules applied through shortest paths are shown with different analysis.

References

[1] Dr.G.Nirmala,P.Sindhamani “Characteristics of fuzzy Petersen graph with fuzzy rule”,journal,2014. [2] Dr.Dr.G.Nirmala,S.Prabavathi “Application of fuzzy if-then rule in Peterson graph”, volume 4,issue 8,August 2014. [3] M.Tamilarasi,Dr.S.S.Dhenakaran “Hamiltonian Approach for shortest path”,IJSRT 184894 June 2018. [4] Sunny Dagar,”Modified prim’s Algorithm” volume 03, volume 02,2012. [5] Dr.DVijayalakshmi,R.Kalaivani “Minimum cost spanning tree using matrix algorithm “Journal.

Copyright

Copyright © 2022 Suguna. R, Naveen. L. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ijraset40273Suguna

Download Paper

Authors : Suguna.R

Paper Id : IJRASET40273

Publish Date : 2022-02-08

ISSN : 2321-9653

Publisher Name : IJRASET

DOI Link : Click Here

About Us

International Journal for Research in Applied Science and Engineering Technology (IJRASET) is an international peer reviewed, online journal published for the enhancement of research in various disciplines of Applied Science & Engineering Technologies.

Quick links
  • Privacy Policy
  • Refund & Cancellation Policy
  • Shipping Policy
  • Terms & Conditions
Quick links
  • Home
  • About us
  • Editorial Board
  • Impact Factor
  • Submit Paper
  • Current Issue
  • Special Issue
  • Pay Fee
  • Topics
Journals for publication of research paper | Research paper publishers | Paper publication sites | Best journal to publish research paper | Research paper publication sites | Journals for paper publication | Best international journal for paper publication | Best journals to publish papers in India | Journal paper publishing sites | International journal to publish research paper | Online paper publishing journal

© , International Journal for Research in Applied Science and Engineering Technology All rights reserved. | Designed by EVG Software Solutions