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| Abstract: | This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis |
| Description: | Department of Mathematics and Statistics,Cochin University of Science & Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3347 |
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| Dyuthi-T1328.pdf | (3.633Mb) |
| URI: | http://dyuthi.cusat.ac.in/purl/1028 |
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| Vijayakumar A 1986.pdf | (373.4Kb) |
| URI: | http://dyuthi.cusat.ac.in/purl/1659 |
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| Dyuthi-T0023.pdf | (3.315Mb) |
| Abstract: | In this thesis an attempt to develop the properties of basic concepts in fuzzy graphs such as fuzzy bridges, fuzzy cutnodes, fuzzy trees and blocks in fuzzy graphs have been made. The notion of complement of a fuzzy graph is modified and some of its properties are studied. Since the notion of complement has just been initiated, several properties of G and G available for crisp graphs can be studied for fuzzy graphs also. Mainly focused on fuzzy trees defined by Rosenfeld in [10] , several other types of fuzzy trees are defined depending on the acyclicity level of a fuzzy graph. It is observed that there are selfcentered fuzzy trees. Some operations on fuzzy graphs and prove that complement of the union two fuzzy graphs is the join of their complements and complement of the join of two fuzzy graphs is union of their complements. The study of fuzzy graphs made in this thesis is far from being complete. The wide ranging applications of graph theory and the interdisciplinary nature of fuzzy set theory, if properly blended together could pave a way for a substantial growth of fuzzy graph theory. |
| URI: | http://dyuthi.cusat.ac.in/purl/43 |
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| Dyuthi-T0027.pdf | (2.557Mb) |
| URI: | http://dyuthi.cusat.ac.in/purl/1698 |
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| Dyuthi-T0259.pdf | (1.520Mb) |
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