本文選題：連通圖 + 正則圖��； 參考：《電子科技大學》2017年碩士論文

【摘要】：近30年以來圖論有了非常快速的發(fā)展,許多工程和應用問題都可以適當?shù)霓D換為圖論問題,并運用圖的理論及其算法對其進行深入的討論和研究。在控制論領域,多智能體網(wǎng)絡中的節(jié)點與鄰節(jié)點間的信息互換通常用圖的理論來建模。多智能體網(wǎng)絡的一致性問題是近年來學者們研究的重點內(nèi)容之一,正是通過對多智能體網(wǎng)絡一致性問題的深入研究而提出了圖的確定一致性猜想。本文主要討論一些特殊的圖是否滿足確定一致性猜想。首先研究了一些非常特殊的圖,如完全圖、樹等,確定其滿足確定一致性猜想,然后討論了直徑與半徑滿足特定關系的圖,研究直徑與半徑在什么關系時該圖滿足確定一致性猜想。對于其它滿足確定一致性猜想的圖的研究難度相對較大,先討論了一些階數(shù)較低的圖,然后探討圖的一些運算對確定一致性猜想的影響。注意到所有的樹都滿足確定一致性猜想,我們以樹圖為基礎構造了一類更廣泛的圖,并且證明了這類圖都滿足確定一致性猜想。本文對圖的確定一致性猜想進行的研究和探討,主要得到了以下結論:首先,證明了所有直徑等于兩倍半徑的圖都滿足確定一致性猜想;從階數(shù)較低的圖出發(fā),證明了五個頂點及以下的所有連通圖都滿足確定一致性猜想。通過分別證明奇數(shù)和偶數(shù)多個頂點的路的情況,證明了所有的路都滿足確定一致性猜想。其次,證明了如果圖G和H都滿足確定一致性猜想,那么G?H也滿足確定一致性猜想。證明了若H是圖G的連通生成子圖,且(7)(8)(7)(8)G(28)H,當H滿足確定一致性猜想時,G也滿足確定一致性猜想。最后,通過對于樹半徑的討論,證明了樹都滿足確定一致性猜想。通過對nH圖的發(fā)散式推廣,構造了一系列特殊的圖并證明這些圖都滿足確定一致性猜想。
[Abstract]:Over the past 30 years, graph theory has developed very rapidly. Many engineering and application problems can be converted into graph theory problems, and the graph theory and its algorithm are used to discuss and study graph theory. In the field of cybernetics, the information exchange between nodes and adjacent nodes in multi-agent networks is usually modeled by graph theory. In recent years, the consistency of multi-agent networks is one of the most important topics of scholars. It is through the in-depth study of the consistency of multi-agent networks that the conjecture of graph consistency is put forward. This paper mainly discusses whether some special graphs satisfy the conjecture of deterministic consistency. In this paper, we first study some very special graphs, such as complete graphs, trees, etc., and determine the conjecture of certain consistency. Then we discuss the graphs whose diameters and radii satisfy a particular relation. When the relation between diameter and radius is studied, the graph satisfies the conjecture of definite consistency. For other graphs satisfying certain conjecture it is relatively difficult to study. First some graphs with lower order are discussed and then the influence of some operations of graphs on determining conjecture is discussed. Note that all trees satisfy the conjecture of deterministic consistency. We construct a more extensive class of graphs based on tree graphs and prove that all of these graphs satisfy the conjecture of deterministic consistency. This paper studies and discusses the conjecture of certain consistency of graphs, and obtains the following conclusions: firstly, it is proved that all graphs with diameters equal to two times radius satisfy the conjecture of deterministic consistency. It is proved that all connected graphs with five vertices and below satisfy the conjecture of deterministic consistency. By proving the paths of odd and even vertices respectively, it is proved that all paths satisfy the conjecture of deterministic consistency. Secondly, it is proved that if the graph G and H satisfy the conjecture of deterministic consistency, then GG H also satisfies the conjecture of deterministic consistency. It is proved that if H is a connected generating subgraph of graph G, and G satisfies the conjecture of certain consistency when H satisfies the conjecture of certain consistency. Finally, by discussing the radius of the tree, it is proved that the tree satisfies the conjecture of deterministic consistency. By generalizing the divergence of NH graphs, a series of special graphs are constructed and proved to satisfy the conjecture of deterministic consistency.
【學位授予單位】：電子科技大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O157.5

【參考文獻】

相關博士學位論文 前1條

1 胡鴻翔;多智能體系統(tǒng)的一致性分析與控制[D];浙江工業(yè)大學;2013年

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本文編號：1830088