| Project/Area Number |
24740070
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
KIMURA Kenji 東京理科大学, 工学部, 助教 (30548152)
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| Project Period (FY) |
2012-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | graph / alliance / defensive alliance / offensive alliance / proscribed vertex / prescribed vertex / グラフ / アルゴリズム |
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| Research Abstract |
We extend the notion of a defensive alliance to it with proscribed and prescribed vertices. We proved some upper bounds of order of a defensive alliance for any pair of a graph, and proscribed and prescribed vertices. If a graph is a tree, then we obtain a new upper bounds of order for a defensive alliance with prescribed vertex. Moreover, if a graph is a tree other than a path, then we obtain a new upper bounds of order for an offensive alliance.
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