article

Global defensive alliances in star graphs

Authors:

Yue-Li WangAuthors Info & Claims

Discrete Applied Mathematics, Volume 157, Issue 8

Pages 1924 - 1931

https://doi.org/10.1016/j.dam.2009.01.005

Published: 01 April 2009 Publication History

Abstract

A defensive alliance in a graph G=(V,E) is a set of vertices S@?V satisfying the condition that, for each v@?S, at least one half of its closed neighbors are in S. A defensive alliance S is called a critical defensive alliance if any vertex is removed from S, then the resulting vertex set is not a defensive alliance any more. An alliance S is called global if every vertex in V(G)@?S is adjacent to at least one member of the alliance S. In this paper, we shall propose a way for finding a critical global defensive alliance of star graphs. After counting the number of vertices in the critical global defensive alliance, we can derive an upper bound to the size of the minimum global defensive alliances in star graphs.

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Cited By

Jesse-Józefczyk K(2019)The possible cardinalities of global secure sets in cographsTheoretical Computer Science10.1016/j.tcs.2011.10.004414:1(38-46)Online publication date: 5-Jan-2019
https://dl.acm.org/doi/10.1016/j.tcs.2011.10.004
Slimani HKheddouci H(2019)Saturated boundary k -alliances in graphsDiscrete Applied Mathematics10.1016/j.dam.2014.11.030185:C(192-207)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.dam.2014.11.030
Lewoń RMałafiejska AMałafiejski M(2016)Global defensive sets in graphsDiscrete Mathematics10.1016/j.disc.2016.01.022339:7(1861-1870)Online publication date: 6-Jul-2016
https://dl.acm.org/doi/10.1016/j.disc.2016.01.022
Show More Cited By

Global defensive alliances in star graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
  2. Mathematical analysis
    1. Numerical analysis

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cover image Discrete Applied Mathematics

Discrete Applied Mathematics Volume 157, Issue 8

April, 2009

306 pages

ISSN:0166-218X

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2009.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 April 2009

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Cited By

Jesse-Józefczyk K(2019)The possible cardinalities of global secure sets in cographsTheoretical Computer Science10.1016/j.tcs.2011.10.004414:1(38-46)Online publication date: 5-Jan-2019
https://dl.acm.org/doi/10.1016/j.tcs.2011.10.004
Slimani HKheddouci H(2019)Saturated boundary k -alliances in graphsDiscrete Applied Mathematics10.1016/j.dam.2014.11.030185:C(192-207)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.dam.2014.11.030
Lewoń RMałafiejska AMałafiejski M(2016)Global defensive sets in graphsDiscrete Mathematics10.1016/j.disc.2016.01.022339:7(1861-1870)Online publication date: 6-Jul-2016
https://dl.acm.org/doi/10.1016/j.disc.2016.01.022
Chang CChia MHsu CKuo DLai LWang F(2012)Global defensive alliances of trees and Cartesian product of paths and cyclesDiscrete Applied Mathematics10.5555/2747475.2747511160:4(479-487)Online publication date: 1-Mar-2012
https://dl.acm.org/doi/10.5555/2747475.2747511

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