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Spectra of related graphs and self-reproducing polyhedra

  • Autores: Eduardo Montenegro, Reinaldo Salazar, David L. Powers
  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 11, Nº. 1, 1992, págs. 1-9
  • Idioma: inglés
  • DOI: 10.22199/S07160917.1992.0001.00002
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  • Resumen
    • 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 truncationsof the polyhedra.

  • Referencias bibliográficas
    • Citas [ 1] Brondsted, A.: An Introduction to Convex Polytopes. Springer, New York, 1983.
    • [ 2] Chartrand, G. and Lesniak, L.: Graphs & Digraphs, second ed. Wadsworth. & Brooks/Cole, Monterey, CA., 1979.
    • [ 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,...
    • [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.

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