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Paper Abstract and Keywords
Presentation 2008-03-10 15:55
Security number for outerplanar graphs
Kyohei Kozawa, Yota Otachi, Koichi Yamazaki (Gunma Univ.) COMP2007-64
Abstract (in Japanese) (See Japanese page) 
(in English) Let $G=(V,E)$ be a graph and $S = \{s_1,s_2,\ldots,s_k\}$ be a subset
of $V$.
An \textit{attack} on $S$ is any $k$ mutually disjoint sets
$\mathscr{A} = \{A_1,A_2,\ldots,A_k\}$ such that
$A_i \subseteq N[s_i] - S$ for $1 \le i \le k$, and
a \textit{defense} of $S$ is any $k$ mutually disjoint sets
$\mathscr{D} = \{D_1,D_2,\ldots,D_k\}$ such that
$D_i \subseteq N[s_i] \cap S$ for $1 \le i \le k$,
where $N[v]$ denotes the closed neighborhood of $v$.
Then attack $\mathscr{A}$ is said to be \textit{defendable}
if there exists a defense $\mathscr{D}$ such that $|D_i| \ge |A_i|$
for $1 \le i \le k$, and
$S$ is \textit{secure} if every attack on $S$ is defendable.
The \textit{security number} of $G$ is the cardinality of
a smallest secure set of $G$.
In this paper, we show that any outerplanar graph has security number
at most 3.
Keyword (in Japanese) (See Japanese page) 
(in English) Outerplanar graph / Security number / / / / / /  
Reference Info. IEICE Tech. Rep., vol. 107, no. 537, COMP2007-64, pp. 63-65, March 2008.
Paper # COMP2007-64 
Date of Issue 2008-03-03 (COMP) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
Copyright
and
reproduction
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee COMP  
Conference Date 2008-03-10 - 2008-03-10 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2008-03-COMP 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Security number for outerplanar graphs 
Sub Title (in English)  
Keyword(1) Outerplanar graph  
Keyword(2) Security number  
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1st Author's Name Kyohei Kozawa  
1st Author's Affiliation Gunma University (Gunma Univ.)
2nd Author's Name Yota Otachi  
2nd Author's Affiliation Gunma University (Gunma Univ.)
3rd Author's Name Koichi Yamazaki  
3rd Author's Affiliation Gunma University (Gunma Univ.)
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Speaker
Date Time 2008-03-10 15:55:00 
Presentation Time 25 
Registration for COMP 
Paper # IEICE-COMP2007-64 
Volume (vol) IEICE-107 
Number (no) no.537 
Page pp.63-65 
#Pages IEICE-3 
Date of Issue IEICE-COMP-2008-03-03 


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