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題名 | The Number of Independent Sets in Forests Having No Isolated Vertices with a Given Size=給定邊數且不具孤立點之林圖獨立集個數 |
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作者 | 周敏貞; 林正忠; Jou, Min-jen; Lin, Jenq-jong; |
期刊 | 嶺東學報 |
出版日期 | 20110600 |
卷期 | 29 2011.06[民100.06] |
頁次 | 頁127-132 |
分類號 | 319.9 |
語文 | eng |
關鍵詞 | 獨立集; 孤立點; 林圖; 極圖; Independent set; Isolated vertex; Forest; Extremal graph; |
中文摘要 | 圖形G=(V, E)中之獨立集爲點集V之一子集合S,且使得S中任兩點在G中均不相連。令F(下標 m)爲具有m條邊且不具孤立點所有林圖所成的集合。在本篇論文中,我們確定了F(下標 m)中獨立集之第一、第二及第三大數值。除此之外,我們亦描繪出達到這些數值之極圖。 |
英文摘要 | In a graph G=(V, E), an independent set is a subset S of V such that no two vertices in S are adjacent. Let F(subscript m) denote the set of forests of size m having no isolated vertices. In this paper, the forests in F(subscript m) with the largest, the second largest and the third largest numbers of independent sets are determined, respectively. We also characterize those extremal graphs achieving these values. |
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