1. Shodhganga@INFLIBNET
  2. Mother Teresa Womens University
  3. Department of Mathematics
Please use this identifier to cite or link to this item: http://hdl.handle.net/10603/303335
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DC FieldValueLanguage
dc.coverage.spatialMathematics
dc.date.accessioned2020-10-19T06:43:24Z-
dc.date.available2020-10-19T06:43:24Z-
dc.identifier.urihttp://hdl.handle.net/10603/303335-
dc.description.abstractIn this research, operations on fuzzy set theory is extended to the fuzzy adjacent matrix of the fuzzy graph. In this process many properties of fuzzy adjacent matrix is discussed. Fuzzy adjacent matrices is probably the most frequently used matrix representation of a fuzzy graph. Fuzzy graph is represented by fuzzy adjacent matrix. It can be manipulated in many ways than a non square matrix. Basic characteristics of the fuzzy adjacent matrix are highlighted. Under max-min and min-max composition several properties of fuzzy adjacent and diagonal degree matrices of fuzzy graph are found. The relation between fuzzy adjacent matrix and diagonal degree matrix of fuzzy graph is discussed. The fuzzy adjacent matrix provides the sound interpretation on the bounds. The energy of the fuzzy graph is calculated using the eigen values of fuzzy adjacent matrix. This enables to determine the bounds and spectra of the fuzzy graph. The condition for the existence of fuzzy walk in a fuzzy graph is captured. The edge sequence, composite fuzzy walk, inverse fuzzy walk and reachability of fuzzy graph is introduced. The necessary condition for existence of fuzzy path in fuzzy walk is given through fuzzy adjacent matrix. Variousresults characterizing fuzzy walk and its varieties with repect to fuzzy graph is given. The strength of a fuzzy walk through fuzzy adjacent matrix is established. The number of edge sequence with reference to fuzzy adjacent matrix under max min composition is proposed. The equivalence relation on fuzzy path is interpreted. The existence of random walk on fuzzy graph is determined with respect to the transition matrix. The random walk is classified into states. Regardless of the original state of a MC, the chain will not enter into an absorbing state in a finite number of steps. The long term trend that depends on the initial state is evaluated. The n step random walk on fuzzy graph is given through max-min and min max composition. The stationary distribution of random walk is found. newline
dc.format.extentiv, 220p.
dc.languageEnglish
dc.relation80 Nos.
dc.rightsuniversity
dc.titleRandom walk on fuzzy graphs
dc.title.alternative-
dc.creator.researcherJayalakshmi, P.
dc.subject.keywordMathematics Applied
dc.subject.keywordPhysical Sciences
dc.description.noteBibliography p.212-219
dc.contributor.guideVimala S.
dc.publisher.placeKodaikanal
dc.publisher.universityMother Teresa Womens University
dc.publisher.institutionDepartment of Mathematics
dc.date.registered2014
dc.date.completed2019
dc.date.awarded2020
dc.format.dimensionsA4
dc.format.accompanyingmaterialDVD
dc.source.universityUniversity
dc.type.degreePh.D.
Appears in Departments:Department of Mathematics

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01_ title.pdfAttached File106.54 kBAdobe PDFView/Open
02-certificate..pdf163.58 kBAdobe PDFView/Open
03_contents..pdf202.03 kBAdobe PDFView/Open
04_chapter 1.pdf445.91 kBAdobe PDFView/Open
05_chapter 2.pdf760.54 kBAdobe PDFView/Open
06_chapter3.pdf946.83 kBAdobe PDFView/Open
07_chapter 4.pdf1.54 MBAdobe PDFView/Open
08_chapter5.pdf1.07 MBAdobe PDFView/Open
09_chapter 6.pdf748.1 kBAdobe PDFView/Open
10_chapter 7.pdf881.2 kBAdobe PDFView/Open
80_recommendation.pdf384.23 kBAdobe PDFView/Open
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