Teoría algebraica de gráficas

Profesor: Dr. Carlos A. Alfaro

"The mathematician’s patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way.
Beauty is the first test: there is no permanent place in this world for ugly mathematics."
G.H. Hardy

Contenido de la materia

  1. Gráficas, matrices y polinomios
    1. matriz de incidencia
    2. matriz de adyacencia
    3. matriz Laplaciana
    4. matriz de distancia
    5. polinomio de Tutte
    6. polinomio cromático
  2. Espectro
    1. matriz de adyacencia
    2. matriz Laplaciana
    3. matriz de distancia
  3. Grupos
    1. automorfismos
    2. pilas de arena

Referencias

  1. R. B. Bapat. Graphs and matrices. Universitext. Springer, London; Hindustan Book Agency, New Delhi, 2010.
  2. Lowell W. Beineke and Robin J. Wilson, editors. Topics in algebraic graph theory, volume 102 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 2004
  3. Norman Biggs. Algebraic graph theory. Cambridge Mathematical Library. Cambridge University Press, Cambridge, second edition, 1993.
  4. Andries E. Brouwer and Willem H. Haemers. Spectra of graphs. Universitext. Springer, New York, 2012.
  5. Dragoš Cvetkovi'c, Peter Rowlinson, and Slobodan Simi'c. An introduction to the theory of graph spectra, volume 75 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 2010.
  6. Chris Godsil and Gordon Royle. Algebraic graph theory, volume 207 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2001.
  7. Caroline J. Klivans. The mathematics of chip-firing. Discrete Mathematics and its Applications (Boca Raton). CRC Press, Boca Raton, FL, 2019.
  8. W. David Joyner and Caroline Grant Melles. Adventures in Graph Theory. Birkhäuser Cham, 2017.

Software

Usaremos SageMath que se puede usar a través de las aplicaciones web SageMathCell o JGraphs.
Un pequeño video-tutorial de JGraphs se encuentra en YouTube.