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題 名 | The Number of Minimal Vertex Covers in the Product of Stars or Paths=星形或路徑乘積圖中最小點覆蓋計數 |
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作 者 | 周敏貞; 林正忠; | 書刊名 | 嶺東學報 |
卷 期 | 23 2008.06[民97.06] |
頁 次 | 頁11-20 |
分類號 | 319.9 |
關鍵詞 | 最小點覆蓋; 乘積; 星形; 路徑; Minimal vertex cover; Product; Star; Path; |
語 文 | 英文(English) |
中文摘要 | 圖形G之點覆蓋,爲G點集之子集合S,且使得圖形G中任一邊的兩個端點,至少有一個屬於S‧若一點覆蓋的子集合均不爲點覆蓋,則稱此點覆蓋爲最小點覆蓋。兩個圖形G和H之(卡式)乘積圖G×H定義爲具有點集V(G)×V(H)且當u1=v1,u2與v2在H中相鄰或當u2=v2,u1與v1在G中相鄰,則稱(u1, u2)與(v1,v2)在G×H中相鄰。在本篇論文中,我們確定了星形或星形與點數不大於5之路徑乘積圖中最小點覆蓋的數目。 |
英文摘要 | Suppose G is a graph. A set S ⊆ V (G) is called a vertex cover of G if each edge of G is incident with at least one vertex of S. A minimal vertex cover is a vertex cover which contains no proper vertex cover. The product (also called cartesian product) G×H of two graphs G and H with vertex sets V (G) and V (H), respectively, has the cartesian product V (G)×V (H) as its set of vertices. Two vertices (u1, u2) and (v1, v2) are adjacent if u1=v1, u2 and v2 are adjacent in H or u2=v2, u1 and v1 are adjacent in G. In this paper, we determine the number of minimal vertex covers in the product of two stars or of a star and a path of order at most 5. |
本系統中英文摘要資訊取自各篇刊載內容。