| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 張原禎 | zh_TW |
| DC.creator | Y-Z Chang | en_US |
| dc.date.accessioned | 2001-7-11T07:39:07Z | |
| dc.date.available | 2001-7-11T07:39:07Z | |
| dc.date.issued | 2001 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN= 88221012 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.abstract | 假設 是一個圖形，如果它的邊有一正實數的加權(也就是存在一個函數 對到正實數)，以 來表示 這個邊的加權，這種圖形我們稱為加權圖，我們以 來表示它。
在連通加權圖上的路徑 ，這條路徑的加權定義為 = 。
對於加權圖 上的兩點 ，這兩點的加權距離定義為 ，這個最小值是在所有連接 的路徑 中取的。
對於加權圖 上的一點 ，這一點的加權和我們定義為 = ，而這個加權圖的和我們將它定義為 。
如果加權圖 上的一點v滿足 ，則我們稱v為此一加權圖的中位點。
如果加權圖的每個邊的加權都是1時，則
在加權圖 中，假設 是 的一個重排函數，則 的加權位移我們定義為 。這個圖形的加權和我們定義為 ，這個最大值是在V(G)的所有重排函數的加權位移取的。
在這篇論文，我們將探討：
1. 中位點在連通加權圖的位置。
2. 有n個點及最大degree為k之連通圖的和之範圍。
3. 加權圖的位移跟和之間的關係。 | zh_TW |
| dc.description.abstract | Suppose that is a graph with positive weights on edges, (i.e, there exists a weight function to R ). w(e) is called the weight on an edge . Then is called a weighted graph.
Suppose that is a connected, weighted graph. For a path in the weight of is defined by = .
For two vertices in the weight distance between x and y is defined by , where the minimum is taken over all paths P which join x and y.
For a vertex x the weight sum of x is = .
The weight sum of a graph is .
If a vertex v satisfies , then v is called a weight median of .
If for every edge in then
Suppose is a permutation of . Then the weight displacement of is defined by .
The weight displacement of is defined by , where the maximum is taken over all permutations of .
In this paper, we consider
1. The locations of weight medians of a connected, weighted graph.
2. The range of if is a connected graph of order n and with maximum degree.
3. The relationship between the weight sum and the weight displacement of a connected graph. | en_US |
| DC.subject | 加權圖 | zh_TW |
| DC.subject | 和 | zh_TW |
| DC.subject | 中位點 | zh_TW |
| DC.subject | 位移 | zh_TW |
| DC.subject | weighted graph | en_US |
| DC.subject | sum | en_US |
| DC.subject | median | en_US |
| DC.subject | displacement | en_US |
| DC.title | 加權圖之和、中位點及位移 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | Sums, Medians and Displacements of Weighted Graphs | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |