Fiedler vector analysis for particular cases of connected graphs
DOI:
https://doi.org/10.22199/issn.0717-6279-4790Keywords:
Spectral graph theory, Fiedler vector, Algebraic connectivity, Block graphsAbstract
In this paper, some subclasses of block graphs are considered in order to analyze Fiedler vector of its members. Two families of block graphs with cliques of fixed size, the block-path and block-starlike graphs, are analyzed. Cases A and B of classification for both families were considered, as well as the behavior of the algebraic connectivity when some vertices and edges are added for particular cases of block-path graphs.
References
N. M. M. Abreu, “Old and new results on algebraic connectivity of graphs”, Linear algebra and its applications, vol. 423, no. 1, pp. 53-73, 2007, https://doi.org/10.1016/j.laa.2006.08.017
A. Brandstädt, V. B. Le, and J. Spinrad, Graph Classes: a survey, Philadelphia, PA: SIAM, 1999. https://doi.org/10.1137/1.9780898719796
M. M.Fiedler, “Algebraic connectivity of graphs”, Czechoslovak mathematical journal, vol. 23, no. 2, pp. 298-305, 1973. [Online] Available: https://bit.ly/3xo8If4
M. M. Fiedler, “A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory”, Czechoslovak mathematical journal, vol. 25, no. 4, pp. 607-618, 1975. [Online] Available: https://bit.ly/3yn36TF
R. Grone and R. Merris, “Characteristic vertices of trees”, Linear and multilinear algebra, vol. 22, no. 2, pp. 115-131, 1987. https://doi.org/10.1080/03081088708817827
S. Kirkland, “Algebraic connectivity,” in Handbook of linear algebra, L. Hogben, R. Brualdi, A. Greenbaum, and R. Mathias, Eds. Boca Raton, FL: Chapman and Hall/CRC, 2006, pp. 36/1-36/12. https://doi.org/10.1201/9781420010572
S. Kirkland, M. Neumann, and B. L. Shader, “Characteristic vertices of weighted trees via Perron values”, Linear and multilinear algebra, vol. 40 no. 4, pp. 311-325, 1996. https://doi.org/10.1080/03081089608818448
S. Kirkland, and S. Fallat, “Perron components and algebraic connectivity for weighted graphs”,Linear and multilinear algebra, vol. 44, no 2, pp. 131-148, 1998, https://doi.org/10.1080/03081089808818554
S. Kirkland, I. Rocha, and V. Trevisan, “Algebraic connectivity of k-connected graphs”. Czechoslovak mathematical journal, vol. 65, pp. 219-236, 2015. https://doi.org/10.1007/s10587-015-0170-9
K. L. Patra, “Maximizing the distance between center, centroid and characteristic set of a tree”, Linear and multilinear algebra, vol. 55, no. 4, pp. 381-397, 2007. https://doi.org/10.1080/03081080701208512
M. Watanabe and A. J. Schwenk, “Integral starlike trees”, Journal of the Australian Mathematical Society, vol. 28, no. 1, pp. 120-128, 1979. https://doi.org/10.1017/S1446788700014981
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