Spectra of related graphs and self-reproducing polyhedra
DOI:
https://doi.org/10.22199/S07160917.1992.0001.00002Keywords:
polyhedronAbstract
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.
References
[ 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, 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.
[ 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, 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.
Published
2018-04-02
How to Cite
[1]
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.
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