本文選題：全控制數(shù)　切入點(diǎn)：零化數(shù)　出處：《新疆大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：上世紀(jì)六十年代以來,圖論作為年輕的數(shù)學(xué)分支,獲得了空前的發(fā)展,在物理學(xué),化學(xué),生物學(xué),網(wǎng)絡(luò)理論,信息科學(xué)以及計算機(jī)科學(xué)等學(xué)科中有著極其廣泛的應(yīng)用.圖論作為組合數(shù)學(xué)的一個分支,受到了各方面的普遍重視.對于任意一個非平凡圖,其全控制數(shù)與零化數(shù)這兩個參數(shù)之間是有關(guān)系的.這兩個參數(shù)在很多領(lǐng)域有著廣泛的應(yīng)用,如利用圖的零化數(shù)計算其獨(dú)立數(shù)的上界等.本文主要研究單圈圖的這兩個參數(shù)之間的關(guān)系.給定一個簡單圖G,γt(G)和a(G)分別表示圖G的全控制數(shù)和零化數(shù).Desormeaux,Haynes和Henning(離散應(yīng)用數(shù)學(xué).161(2013)349-354)提出了一個猜想:如果圖G是一個頂點(diǎn)數(shù)為n的連通非平凡圖,是否有γt(G)≤a(G)+1成立?他們證明了對于任意一個非平凡樹T,此猜想是成立的.在本文中,我們證明了對于一個頂點(diǎn)數(shù)為n的連通單圈圖G,則γt(G)≤a(G)+1,等號成立當(dāng)且僅當(dāng)G～=Cn且n不被4整除.
[Abstract]:Since -40s, as a young branch of mathematics, graph theory has gained unprecedented development in physics, chemistry, biology, network theory, As a branch of combinatorial mathematics, graph theory is widely used in the fields of information science and computer science. There is a relationship between the total domination number and the zero number. These two parameters are widely used in many fields. For example, the upper bound of the independent number of a graph is calculated by using the zeroing number of a graph. In this paper, the relationship between these two parameters of a unicyclic graph is studied. Given a simple graph G, 緯 t0 G) and a G), respectively, the total domination number and zero number of graph G are denoted by the total domination number and zero number. Desormeaux.Haynes and Henning. In this paper, we present a conjecture: if G is a connected nontrivial graph with n vertices, Is there a 緯 TX G) 鈮，

本文編號：1576154