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題 名 | The Number of Maximal Independent Sets in Triangle-Free Quasi-Tree Graphs=無3迴圈準樹圖中最大獨立集之個數 |
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作 者 | 周敏貞; 林正忠; | 書刊名 | 嶺東學報 |
卷 期 | 39 2016.06[民105.06] |
頁 次 | 頁75-93 |
分類號 | 319.76 |
關鍵詞 | 最大獨立集; 無3迴圈; 樹圖; 林圖; 準樹圖; 準林圖; 極圖; Maximal independent set; Triangle-free; Tree; Forest; Quasi-tree graph; Quasi-forest graph; Extremal graph; |
語 文 | 英文(English) |
中文摘要 | 若一獨立集不為其他獨立集之真子集,則稱此獨立集為最大獨立集。一個具有點集V (G) 的連通圖形G(圖形G),若存在點x ∈V (G) 使得G-x 為樹圖(林圖),則稱G 為準樹圖(準林圖)。本篇論文目的在於找到了所有不具有邊數為3 之迴圈的準樹圖(準林圖)中最大獨立集之最大數值。除此之外,我們亦描繪出達到此值之所有極圖。 |
英文摘要 | A maximal independent set is an independent set that is not a proper subset of any other independent set. A connected graph (respectively, graph) G with vertex set V(G) is called a quasi -tree graph (respectively, quasi-forest graph), if there exists a vertex x ∈V ( G) such that G - x is a tree (respectively, forest) . The purpose of this paper is to determine the largest number of maximal independent sets among all quasi- tree graphs and quasi -forest graphs containing no cycle of length three, respectively. Additionally, extremal graphs achieving these values are also given. |
本系統中英文摘要資訊取自各篇刊載內容。