Global Defensive Alliances in Wheel Graphs and Complementary Prisms
Abstract
Graphs are very useful and it helps solving problems. A relatively new that has been studied is alliances in graphs. In this paper, it is studied the defensive alliances, which can be used as a mathematical model in web communities, social medias, chain food, etc. It was found results in wheel graphs and complementary prisms of complete graphs.
Keywords:
Graphs, Defensive Alliances, Web Communities, Social Networks.
References
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Brigham, R. C., Dutton, R. D., Haynes, T. W. and Hedetniemi, S. T. (2009). Powerful alliances in graphs. Discrete Mathematics, Elsevier, pages 2140 – 2147.
Chang, C. W., Chia, M. L., Hsu, C. J., Kuo, D. and Lai, L. L. (2012). Global defen-sive alliances of trees and Cartesian product of paths and cycles. Discrete Applied Mathematics, pages 160:479 – 487.
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Dourado, M. C., Faria, L., Pizana, M. A., Rautenbach, D. and Szwarcfiter, J. L. (2014). On defensive alliances and strong global offensive alliances. Discrete Applied Mathematics, pages 163:136 – 141.
Favaron, O., Fricke, G., Goddard, W., Hedetniemi, S. M., Hedetniemi, S. T., Kristiansen, T., Laskar, R. C. and Skaggs, R. D. (2004). Offensive Alliances in Graphs. Discussio-nes Mathematicae, Graph Theory, pages 24:263 – 275.
Goddard, W. and Henning, M. (2013). Independent domination in graphs: A survey and recent results. Discrete Mathematics, pages 313:839 – 854.
Gonçalves, B. C. (2016). Aliançaas defensivas globais em alguns produtos de grafos. Technical report, Instituto de Informática, Universidade Federal de Goiás, Goiânia.
Haynes, T. W.; Henning, M. A. and van der Merwe, L. C. (2008) Domination and total domination in complementary prisms. J. Combin. Optimization, Springer Netherlands.
Hedetniemi, S., Hedetniemi, S. and Kristiansen, P. (2004). Alliances in graphs. Journal of Combinatorial Mathematics and Combinatorial Computing, pages 157 – 177.
Rosen, K. H. (2009). Matemática Discreta e Suas Aplicações. McGraw-Hill, 6th edition, pages 589 – 675.
Shafique, K. H. (2004). Partitioning a Graph in Alliances and its Application to Data Clustering. PhD thesis, School of Computer Science, University of Central Florida, Orlando.
Silva, L. R. S. da (2015). Sobre Alianças Defensivas e Ofensivas Globais em Alguns Produtos de Grafos e Grafos Simpliciais. PhD thesis, Instituto de Informática, Universidade Federal de Goiás. Goiânia.
Yero, I. G. and Rodríguez-Velazquez, J. A. (2013). Defensive alliances in graphs: a survey. PhD thesis, Departamento de Matemáticas, Escuela Politécnica Superior de Algeciras, Universidad de Cádiz. Espanha.
Brigham, R. C., Dutton, R. D., Haynes, T. W. and Hedetniemi, S. T. (2009). Powerful alliances in graphs. Discrete Mathematics, Elsevier, pages 2140 – 2147.
Chang, C. W., Chia, M. L., Hsu, C. J., Kuo, D. and Lai, L. L. (2012). Global defen-sive alliances of trees and Cartesian product of paths and cycles. Discrete Applied Mathematics, pages 160:479 – 487.
Dias, E. S. (2012). Alianças defensivas em grafos, volume 1. Editora UFG, 1st edition.
Dourado, M. C., Faria, L., Pizana, M. A., Rautenbach, D. and Szwarcfiter, J. L. (2014). On defensive alliances and strong global offensive alliances. Discrete Applied Mathematics, pages 163:136 – 141.
Favaron, O., Fricke, G., Goddard, W., Hedetniemi, S. M., Hedetniemi, S. T., Kristiansen, T., Laskar, R. C. and Skaggs, R. D. (2004). Offensive Alliances in Graphs. Discussio-nes Mathematicae, Graph Theory, pages 24:263 – 275.
Goddard, W. and Henning, M. (2013). Independent domination in graphs: A survey and recent results. Discrete Mathematics, pages 313:839 – 854.
Gonçalves, B. C. (2016). Aliançaas defensivas globais em alguns produtos de grafos. Technical report, Instituto de Informática, Universidade Federal de Goiás, Goiânia.
Haynes, T. W.; Henning, M. A. and van der Merwe, L. C. (2008) Domination and total domination in complementary prisms. J. Combin. Optimization, Springer Netherlands.
Hedetniemi, S., Hedetniemi, S. and Kristiansen, P. (2004). Alliances in graphs. Journal of Combinatorial Mathematics and Combinatorial Computing, pages 157 – 177.
Rosen, K. H. (2009). Matemática Discreta e Suas Aplicações. McGraw-Hill, 6th edition, pages 589 – 675.
Shafique, K. H. (2004). Partitioning a Graph in Alliances and its Application to Data Clustering. PhD thesis, School of Computer Science, University of Central Florida, Orlando.
Silva, L. R. S. da (2015). Sobre Alianças Defensivas e Ofensivas Globais em Alguns Produtos de Grafos e Grafos Simpliciais. PhD thesis, Instituto de Informática, Universidade Federal de Goiás. Goiânia.
Yero, I. G. and Rodríguez-Velazquez, J. A. (2013). Defensive alliances in graphs: a survey. PhD thesis, Departamento de Matemáticas, Escuela Politécnica Superior de Algeciras, Universidad de Cádiz. Espanha.
Published
2018-08-08
How to Cite
FREITAS, Rafael de Castro; DIAS, Elisângela Silva.
Global Defensive Alliances in Wheel Graphs and Complementary Prisms. In: REGIONAL SCHOOL ON INFORMATICS OF GOIÁS (ERI-GO), 2018. , 2018, Goiânia.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2018
.
p. 283-292.
