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Properties of Zero-divisor Graph of Zn[i]

Author: LiXiangNi
Tutor: TangGaoHua
School: Guangxi Normal University
Course: Basic mathematics
Keywords: Zero Factor Zero factor graph Class number Number of support Independence number Connectivity Chromatic number
CLC: O157.5
Type: Master's thesis
Year: 2010
Downloads: 28
Quote: 1
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Abstract


Ring theory and graph theory in mathematics in two very important branch , they are not only rich in content , but also in many other branches of mathematics ( eg combinatorial mathematics , geometry, automata theory and coding theory , etc. ) also has an important role. Ring zero divisor graph , chart properties are mainly using algebraic system , it provides a new method of mathematical problems . Zero- divisor graph of the ring is the last two decades has generated a new field of study, raises a lot of interesting results and problems. Over the past decade , it has become a popular international research field . Gaussian integers modulo n ring Z_n [i] is a very important ring of a ring , is often discussed as examples in abstract algebra . This paper uses commutative algebra , modern algebra and graph theory knowledge and methods , research Г (Z_n [i]) and some properties of its complement . The first chapter , an overview of the history of the development of zero- divisor graph , the research background and the main results of this paper , while we also give ring theory and graph theory , some basic concepts and conclusions. Chapter II , research Gaussian integers modulo n ring Z_n [i] zero- divisor graph of categories, and gives Z_n [i] when is complete and in this case Z_n [i] zero point factor graph coloring number. Chapter III of Gaussian integers modulo n ring Z_n [i] zero- divisor graph of support and in some cases the number of independent number. Chapter IV , research Gaussian integers modulo n ring Z_n [i] zero factor complement graph connectivity and class number .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
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