Spectral study of alliances in graphs

Juan Alberto Rodríguez-Velazquez; Jose Maria Sigarreta Almira

Discussiones Mathematicae Graph Theory (2007)

  • Volume: 27, Issue: 1, page 143-157
  • ISSN: 2083-5892

Abstract

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In this paper we obtain several tight bounds on different types of alliance numbers of a graph, namely (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the relationship between the alliance numbers of a graph and its algebraic connectivity, its spectral radius, and its Laplacian spectral radius.

How to cite

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Juan Alberto Rodríguez-Velazquez, and Jose Maria Sigarreta Almira. "Spectral study of alliances in graphs." Discussiones Mathematicae Graph Theory 27.1 (2007): 143-157. <http://eudml.org/doc/270508>.

@article{JuanAlbertoRodríguez2007,
abstract = {In this paper we obtain several tight bounds on different types of alliance numbers of a graph, namely (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the relationship between the alliance numbers of a graph and its algebraic connectivity, its spectral radius, and its Laplacian spectral radius.},
author = {Juan Alberto Rodríguez-Velazquez, Jose Maria Sigarreta Almira},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {defensive alliance; offensive alliance; dual alliance; domination; spectral radius; graph eigenvalues.; graph eigenvalues},
language = {eng},
number = {1},
pages = {143-157},
title = {Spectral study of alliances in graphs},
url = {http://eudml.org/doc/270508},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Juan Alberto Rodríguez-Velazquez
AU - Jose Maria Sigarreta Almira
TI - Spectral study of alliances in graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2007
VL - 27
IS - 1
SP - 143
EP - 157
AB - In this paper we obtain several tight bounds on different types of alliance numbers of a graph, namely (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the relationship between the alliance numbers of a graph and its algebraic connectivity, its spectral radius, and its Laplacian spectral radius.
LA - eng
KW - defensive alliance; offensive alliance; dual alliance; domination; spectral radius; graph eigenvalues.; graph eigenvalues
UR - http://eudml.org/doc/270508
ER -

References

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  1. [1] M. Fiedler, A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory, Czechoslovak Math. J.25 (100) (1975) 619-633. Zbl0437.15004
  2. [2] S.M. Hedetniemi, S.T. Hedetniemi and P. Kristiansen, Alliances in graphs, J. Combin. Math. Combin. Comput. 48 (2004) 157-177. Zbl1051.05068
  3. [3] T.W. Haynes, S.T Hedetniemi and M.A. Henning, Global defensive alliances in graphs, Electron. J. Combin. 10 (2003), Research Paper 47, 13 pp. Zbl1031.05096
  4. [4] J.A. Rodríguez, Laplacian eigenvalues and partition problems in hypergraphs, submitted. 
  5. [5] J.A. Rodríguez and J.M. Sigarreta, Global alliances in planar graphs, submitted. Zbl1135.05052

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