Title

Security in graphs

Authors

Authors

R. C. Brigham; R. D. Dutton;S. T. Hedetniemi

Comments

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Abbreviated Journal Title

Discret Appl. Math.

Keywords

alliances; defensive alliances; Mathematics, Applied

Abstract

Let G = (V, E) be a graph. A set S subset of V is a defensive alliance if vertical bar N[x] boolean AND S vertical bar >= vertical bar N[x] - S vertical bar for every x epsilon S. Thus, each vertex of a defensive alliance can, with the aid of its neighbors in S, be defended from attack by its neighbors outside of S. An entire set S is secure if any subset X subset of S can be defended from an attack from outside of S, under an appropriate definition of what such a defense implies. Necessary and sufficient conditions for a set to be secure are determined. Published by Elsevier B.V.

Journal Title

Discrete Applied Mathematics

Volume

155

Issue/Number

13

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

1708

Last Page

1714

WOS Identifier

WOS:000249236300006

ISSN

0166-218X

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