### 博碩士論文 88221012 詳細資訊

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(Sums, Medians and Displacements of Weighted Graphs)

 ★ 圖之均勻分解與有向圖之因子分解 ★ 迴圈之冪圖的星林分解數 ★ 圖形的線性蔭度及星形蔭度 ★ On n-good graphs ★ A Note On Degree-Continuous Graphs ★ Status Sequences and Branch-Weight Sequences of Trees ★ n-realizable Quadruple ★ 圖形的路徑分解,迴路分解和星形分解 ★ 星林圖的二分解與三分解 ★ 2-decomposable, 3-decomposable multipaths and t-decomposable spiders ★ 圖形分解與反魔圖 ★ The antimagic graph with a generalization ★ 圖的程度序列和狀態 ★ The 3-split of multipaths and multicycles with multiplicity 2 ★ 圖形之分割與反魔標號

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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。

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.

★ 和
★ 中位點
★ 位移

★ sum
★ median
★ displacement

SECTION 1 INTRODUCTION…………………………………………………? 1
SECTION 2 MEDIANS ………………………………………………………… 2
SECTION 3 SUMS AND EXTREMAL GRAPHS……………………………… 12
SECTION 4 DISPLACEMENTS OF WEIGHTED GRAPH…………………… 24
REFERENCE …………………………………………………………………… 32

(1975) no. 1, 18-20 .
[2] H.-Y. Lee and G.J. Chang, The w-median of a connected strongly graph, J. Graph Theory 18 (1994) 673-680.
[3] M. Truszczynski, Centers and centroids of unicyclic graphs. Math. Slovaca 35 (1985) 223-228.
[4] H. Wittenberg, Local medians in chordal graphs. Disc. Appl. Math. 28 (1990) 287-296.
[5]} S.V. Yushmanov, The median of the Ptolemy graph. Issled.-Operatsii-i-ASU
[Kievskii-Gosudarstvennyi-Universiet.-Issledovanie-Operatsii-i-ASU] No. 32 (1988) 67-70, 118.
[6] B. Zelinka, Medians and peripherians of trees, Arch. Math. 4 (Brno) 1968, 87-95.