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| 題名: | Global defensive alliances of trees and Cartesian product of paths and cycles |
| 作者: | ang, CW (Chang, Chan-Wei)
Chia, ML (Chia, Ma-Lian)
Hsu, CJ (Hsu, Cheng-Ju)
Kuo, D (Kuo, David)
Lai, LL (Lai, Li-Ling)
Wang, FH (Wang, Fu-Hsing) |
| 貢獻者: | Dept Informat Management |
| 關鍵詞: | Global defensive alliance
Tree
Cartesian product
Path
Cycle |
| 日期: | 2012-03 |
| 上傳時間: | 2013-02-22 14:38:53 (UTC+8) |
| 摘要: | Given a graph G. a defensive alliance of G is a set of vertices S subset of V(G) satisfying the condition that for each v epsilon S. at least half of the vertices in the closed neighborhood of v are in S. A defensive alliance S is called global if every vertex in V(G) - S is adjacent to at least one member of the defensive alliance S. The global defensive alliance number of G. denoted gamma(a)(G), is the minimum size around all the global defensive alliances of G. In this paper, we present an efficient algorithm to determine the global defensive alliance numbers of trees, and further give formulas to decide the global defensive alliance numbers of complete k-ary trees for k = 2, 3, 4. We also establish upper bounds and lower bounds for gamma(a)(P-m x P-n), gamma(a)(C-m x P-n) and gamma(a)(C-m x C-n), and show that the bounds are sharp for certain m, n. (c) 2011 Elsevier B.V. All rights reserved. |
| 關聯: | DISCRETE APPLIED MATHEMATICS 卷: 160 期: 4-5 頁數: 479-487 |
| 顯示於類別: | [資訊管理學系暨資訊管理研究所 ] 期刊論文
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