【作者】 王海霞；

【导师】 于洪全；

【作者基本信息】 大连理工大学 ， 基础数学， 2008， 硕士

【摘要】 本文主要主研究图的控制参数．控制参数因为在实际生活中应用的重要性，得到广泛的研究和发展．本文主要包括以下4个方面的工作：(1)简要叙述了图的基本概念及控制参数的发展．(2)介绍了图的几类控制参数，控制数，独立控制数，无赘数，k-控制参数以及其它常见控制函数的基本概念及重要定理．(3)介绍控制参数之间的一些关系．如γ(T)=i(T)及γ(T)≡i(T)时图的特征，以及γ(G)=i(G)且控制集唯一时图的性质．(4)介绍控制参数与图中不变量n，△的关系．刻画了i(T)=n-△，γ(T)=n-△时树的特征，并得到了的结构．结论如下：(a)i(T)=n-△当且仅当树以△为根，树高至多为2，并且|C|≤△-1．(b)γ(T)=n-△当且仅当树为受伤的蜘蛛树．(c)γ(T)=i(T)=n-△当且仅当树为受伤的蜘蛛树．更多还原

【Abstract】 Domination parameters in graphs have been studied extensively due to their intrinsic importance in the study of the graph theory and applications. This thesis discusses the properties of various domination parameters and their relationship.It is divided into 4 parts.(1) We introduce the basic concepts of the graph and the development of the domination theory.(2) We introduce the concepts of the domination number,independence domination num-ber,irredundance number and some other dominaion functions.(3) We introduce the relationship of parameters,such as the characterization of the tree whenγ(T) = i(T) andγ(T) = i(T),we also give the properties of the graph whenγ(G) = i(G) andγ(G) is unique.(4) We introduce the reltation between domination number,n andΔ. We give characterization of trees such that i(T) = n -Δ,γ(T) = n -Δ. it is shown that:(a) i(T) = n -Δif and only if the tree is rooted at A,the height of the tree is no more than 2,and|C|≤Δ-1.(b)γ(T) = n -Δif and only if the tree is a wounded spider.(c)γ(T) = i(T) = n -Δif and only if the tree is a wounded spider.更多还原