On the characteristic polynomial of the power of a path.


  • Beatriz Malajovich Universidade Federal do Estado do Rio de Janeiro.
  • Nair Abreu Universidade Federal do Rio de Janeiro.
  • Lilian Markenzon Universidade Federal do Rio de Janeiro.


Power of a path, 4-cycles, Characteristic coefficients


We determine a closed-form expression for the fifth characteristic coefficient of the power of a path. To arrive at this result, we establish the number of 4-cycles in the graph by means of their structural properties. The method developed might be applied to other well-structured graph classes in order to count 4-cycles or modified to count cycles of different length.

Author Biographies

Beatriz Malajovich, Universidade Federal do Estado do Rio de Janeiro.


Nair Abreu, Universidade Federal do Rio de Janeiro.


Lilian Markenzon, Universidade Federal do Rio de Janeiro.



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How to Cite

B. Malajovich, N. Abreu, and L. Markenzon, “On the characteristic polynomial of the power of a path.”, Proyecciones (Antofagasta, On line), vol. 36, no. 3, pp. 529-543, Oct. 2017.