Title

On a graph's security number

Authors

Authors

R. D. Dutton

Comments

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Abbreviated Journal Title

Discret. Math.

Keywords

Alliances; Secure sets; Mathematics

Abstract

A secure set S subset of V of graph G = (V. E) is a set whose every nonempty subset can be successfully defended from an attack, under appropriate definitions of "attack" and "defended." The set S is secure when vertical bar N[X]boolean AND S vertical bar >= vertical bar N[X] - S vertical bar for every X subset of S. The smallest cardinality of a secure set in G is the security number of G. New bounds for the security number are established, the effect of some graph modifications on the security number is investigated, and the exact value of the security number for some families of graphs is given. (C) 2009 Elsevier B.V. All rights reserved.

Journal Title

Discrete Mathematics

Volume

309

Issue/Number

13

Publication Date

1-1-2009

Document Type

Article

Language

English

First Page

4443

Last Page

4447

WOS Identifier

WOS:000266760400028

ISSN

0012-365X

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