Title

On A Graph'S Security Number

Keywords

Alliances; Secure sets

Abstract

A secure set S ⊆ 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 | N [X] ∩ S | ≥ | N [X] - S | for every X ⊆ 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. © 2009 Elsevier B.V. All rights reserved.

Publication Date

7-6-2009

Publication Title

Discrete Mathematics

Volume

309

Issue

13

Number of Pages

4443-4447

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.disc.2009.02.005

Socpus ID

67349096285 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/67349096285

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