本文選題：關(guān)聯(lián)控制 + 關(guān)聯(lián)加強(qiáng)��； 參考：《山東科技大學(xué)》2017年碩士論文

【摘要】：圖的理論知識(shí)論從誕生之日到目前為止已經(jīng)歷經(jīng)了近三個(gè)世紀(jì)的歲月。圖的著色理論經(jīng)歷了從點(diǎn)到邊,再到特殊的這樣一個(gè)進(jìn)化的過程。那么,控制理論作為圖論中及其重要的一環(huán),也會(huì)經(jīng)歷這樣的過程。于是圖的控制理論開始從點(diǎn)萌發(fā),經(jīng)歷了過對(duì)邊的研究。隨著對(duì)經(jīng)典控制理論研究的加深,加上現(xiàn)實(shí)中的實(shí)際情況提出的具體要求,科學(xué)家們提出了各種各樣的控制理論,經(jīng)典控制理論是基礎(chǔ)(這些理論要么是通過對(duì)經(jīng)典控制的演化而來的,要么是對(duì)經(jīng)典控制施加相應(yīng)的限制因素)本文主要研究圖的關(guān)聯(lián)控制的穩(wěn)定性并給出了部分圖的關(guān)聯(lián)控制數(shù)(控制參數(shù)就是所對(duì)應(yīng)的最小控制集元素的數(shù)目。在對(duì)參數(shù)的探索過程中,一定會(huì)重點(diǎn)探究最小的控制集的相關(guān)性質(zhì),并且會(huì)探究它所對(duì)應(yīng)的參數(shù))。將關(guān)聯(lián)控制的概念與加強(qiáng)數(shù)和約束數(shù)的概念進(jìn)行融合,提出關(guān)聯(lián)加強(qiáng)數(shù)和關(guān)聯(lián)約束數(shù)的定義。關(guān)聯(lián)控制的穩(wěn)定性由關(guān)聯(lián)加強(qiáng)數(shù)和關(guān)聯(lián)約束數(shù)來體現(xiàn)。Fink在第一次提出使用約束數(shù)來計(jì)算互連網(wǎng)絡(luò)的穩(wěn)定性。在互聯(lián)網(wǎng)絡(luò)(圖)中至少刪除幾條邊,才會(huì)讓互聯(lián)網(wǎng)絡(luò)(圖)控制參數(shù)變大,此時(shí)去掉的邊數(shù)就是約束數(shù)。由于控制數(shù)與關(guān)聯(lián)控制數(shù)已確定為N-P問題,故而關(guān)聯(lián)加強(qiáng)數(shù)和關(guān)聯(lián)約束數(shù)也是N-P問題,本文給出幾種特殊圖的關(guān)聯(lián)加強(qiáng)數(shù)和關(guān)聯(lián)約束數(shù)的確切值。
[Abstract]:The theory of graph theory has gone through nearly three centuries since its birth. The coloring theory of graphs has undergone a process of evolution from point to edge and then to a special one. Then, as an important part of graph theory, control theory also goes through this process. So the control theory of graph began to germinate from the point and experienced the research of the opposite side. With the deepening of the study of classical control theory and the specific requirements of the actual situation in reality, scientists have put forward a variety of control theories. Classical control theories are fundamental (these theories are either derived from the evolution of classical control, In this paper, we mainly study the stability of the associated control of graphs and give the associated control number of some graphs (the control parameter is the number of the corresponding minimum control set elements). In the process of exploring the parameters, we will focus on the properties of the smallest control set and the corresponding parameters. The concept of association control is fused with the concepts of reinforcement number and constraint number, and the definition of association strengthening number and associated constraint number is proposed. The stability of the correlation control is represented by the correlation enhancement number and the correlation constraint number. In the first time, Fink proposed the use of the constraint number to calculate the stability of the interconnection network. Only when at least a few edges are deleted in the Internet (graph), the control parameters of the Internet (graph) become larger, and the number of edges removed is the number of constraints. Because the control number and the correlation control number have been determined to be N-P problem, so the correlation enhancement number and the correlation constraint number are also N-P problems. In this paper, the exact values of the association strengthening number and the correlation constraint number of several special graphs are given.
【學(xué)位授予單位】：山東科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前9條

1 徐保根;;關(guān)于圖符號(hào)的邊控制[J];數(shù)學(xué)研究與評(píng)論;2007年01期

2 張忠輔,陳祥恩,李敬文,姚兵,呂新忠,王建方;關(guān)于圖的鄰點(diǎn)可區(qū)別全染色[J];中國(guó)科學(xué)(A輯:數(shù)學(xué));2004年05期

3 徐保根;關(guān)于圖的符號(hào)星控制數(shù)[J];華東交通大學(xué)學(xué)報(bào);2004年04期

4 劉西奎,李艷,許進(jìn);基于遺傳算法的圖關(guān)聯(lián)著色算法[J];工程數(shù)學(xué)學(xué)報(bào);2004年01期

5 王小斌;極大外平面圖的關(guān)聯(lián)色數(shù)[J];數(shù)學(xué)研究;2003年02期

6 陳學(xué)剛,陳東靈;三類笛卡爾積圖的關(guān)聯(lián)色數(shù)[J];經(jīng)濟(jì)數(shù)學(xué);2002年03期

7 王淑棟,龐善臣,劉西奎;高度圖的關(guān)聯(lián)色數(shù)[J];數(shù)學(xué)研究;2001年03期

8 陳學(xué)剛,陳東靈,王淑棟;路與完全圖的笛卡爾積圖和廣義圖K(n,m)的關(guān)聯(lián)色數(shù)[J];經(jīng)濟(jì)數(shù)學(xué);2000年03期

9 陳東靈,劉西奎,王淑棟;圖的關(guān)聯(lián)色數(shù)和關(guān)聯(lián)著色猜想[J];經(jīng)濟(jì)數(shù)學(xué);1998年03期

相關(guān)碩士學(xué)位論文 前4條

1 帥春萍;關(guān)于圖的幾類特殊控制的研究[D];華東交通大學(xué);2009年

2 王文麗;關(guān)于幾類圖的鄰點(diǎn)可區(qū)別關(guān)聯(lián)色數(shù)的研究[D];山東科技大學(xué);2009年

3 周薇;若干圖的關(guān)聯(lián)著色與鄰點(diǎn)可區(qū)別關(guān)聯(lián)著色研究[D];山東科技大學(xué);2009年

4 王雅琴;圖的關(guān)聯(lián)著色與鄰點(diǎn)可區(qū)別關(guān)聯(lián)著色[D];山東科技大學(xué);2007年

，

本文編號(hào)：2053309