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The Study of Some Types of Domination Parameters of Graphs

Author: SunGuiYan
Tutor: ChenXueGang；LiuXiKui
School: Shandong University of Science and Technology
Course: Probability Theory and Mathematical Statistics
Keywords: domination number restrained domination number connected restrained domination number tree restrained domination number signed domination number signed edge domination number minus dommation number
CLC: O157.5
Type: Master's thesis
Year: 2008
Downloads: 7
Quote: 0
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Abstract


Because the search on the domination number is more and more attached importance to people get more deeply aware of it and put forward many domination parameters,such as: domination number,total restrained domination number,signed domination number,signed edge domination number,signed total domination number,and so on.Those types of domination number play an important role in structure of graphs.In this paper we pay our attention mainly on the following parts:In the chapter three and chapter four,we define two new classes of domination:connected restrained domination number and tree restrained domination number.Firstly,we discuss the bounds of them,and then the necessary and sufficient conditions forγr（G）=γrtr（G） andγrt（G）=γrtr（G） are given.In chapter five,we give some better bounds of signed total domination numberγst（G）for small degree graphs with the similar methords in[16].The results are:IfΔ≤4 and d1=0,thenγst（G）≥n/3,and the bound is sharp.If 4≤δ≤Δ≤5,thenγst（G）≥n/5,and the bound is sharp.Also,we connect signed domination number with the signed edgedomination number by the definition of linear graph,further,give some lower bounds ofγs（G）.In the chapter six,we give a bound of minus domination number about maximum degreeΔand minimum degreeδ:γ-（G）≥（δ-Δ+2）/（Δ+δ+2） n.

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