Spectra of related graphs and self-reproducing polyhedra


  • Eduardo Montenegro Universidad Católica de Valparaíso.
  • Reinaldo Salazar Universidad Católica de Valparaíso.
  • David L. Powers Clarkson University.






lf G is a d-valent graph, the eigenvalues of the adjacency matrix of G determine those of the line graph, the subdivision graph and the graph made by replacing vertices with complete graphs. A property of the eigenvectors of the graphs of certain regular polyhedra is then seen to carry over to some truncations
of the polyhedra.

Author Biographies

Eduardo Montenegro, Universidad Católica de Valparaíso.

Instituto de Matemáticas.

Reinaldo Salazar, Universidad Católica de Valparaíso.

Instituto de Matemáticas.

David L. Powers, Clarkson University.

Department of Mathematics & Computer Science.


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[ 3] Coxeter, H.S.M.: Regular Polytopes, third ed. Dover, New York, 1973.

[ 4] Cvetkovic, D.M.; Doob, M. and Sachs, H.: Spectra of Graphs. VEB, Berlin/Academic Press, New York, 1980.

[ 5] Godsil, G.: Graphs, groups and polytopes. In Combinatorial Mathematics VI(Canberra 1977), D.A. Holton and J. Seberry, eds. Springer, New York, pp. 157-164, 1978.

[6] Licata, C. and Powers, D.L.: A surprising property of some regular polytopes. Scientia, 1, pp 73-80, 1988.

[7] Montenegro, E.: A result on the order and size of graphs that represent a finite group. Extracta Mathematicae, 2, pp 14-16, 1987.



How to Cite

E. Montenegro, R. Salazar, and D. L. Powers, “Spectra of related graphs and self-reproducing polyhedra”, Proyecciones (Antofagasta, On line), vol. 11, no. 1, pp. 1-9, Apr. 2018.