Fiedler vector analysis for particular cases of connected graphs

• Traciná, Daniel ^[1] ; Justel, Claudia ^[2]
  1. [1] Pós-graduação em Sistemas e Computação - Instituto Militar de Engenharia
  2. [2] Instituto Militar de Engenharia.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 4, 2021, págs. 1041-1051
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4790
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• Resumen

  • 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.

• Referencias bibliográficas
  • 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,...
  • 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:...
  • M. M. Fiedler, “A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory”, Czechoslovak mathematical...
  • 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,...
  • S. Kirkland, M. Neumann, and B. L. Shader, “Characteristic vertices of weighted trees via Perron values”, Linear and multilinear algebra,...
  • S. Kirkland, and S. Fallat, “Perron components and algebraic connectivity for weighted graphs”,Linear and multilinear algebra, vol. 44, no...
  • S. Kirkland, I. Rocha, and V. Trevisan, “Algebraic connectivity of k-connected graphs”. Czechoslovak mathematical journal, vol. 65, pp. 219-236,...
  • K. L. Patra, “Maximizing the distance between center, centroid and characteristic set of a tree”, Linear and multilinear algebra, vol. 55,...
  • M. Watanabe and A. J. Schwenk, “Integral starlike trees”, Journal of the Australian Mathematical Society, vol. 28, no. 1, pp. 120-128, 1979....