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The Categorical Product of Graphs

Published online by Cambridge University Press:  20 November 2018

Donald J. Miller
Donald J. Miller*
Affiliation:
McMaster University, Hamilton, Ontario; University of Waterloo, Waterloo, Ontario
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Undirected graphs and graph homomorphisms as introduced by Sabidussi (6, p. 386), form a category that admits a categorical product. For the category of graphs and full graph homomorphisms, the categorical product was introduced by Čulik (1) under the name cardinal product. It was independently defined by Weichsel (8) who called it the Kronecker product and investigated the connectedness of products of finitely many factors. Hedetniemi (4) was the first to make use of the fact that the cardinal product is categorical.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1511 - 1521
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

*

The content of this paper is based on part of the author's doctoral thesis written at McMaster University under the direction of Professor G. Sabidussi.

*

I wish to express my gratitude to Professor G. Sabidussi for his valuable suggestions and assistance in the preparation of this work.

References

1. Čulik, K., Zur Théorie der Graphen, Časopis Pest. Mat. 83 (1958), 133–155.Google Scholar
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3. Hedetniemi, Stephen T., Homomorphisms of graphs (University of Michigan Technical Report 03105–42-T, December, 1965; it is stated there that “the complete report is available in the major Navy technical libraries and can be obtained from the Defense Documentation Center“).Google Scholar
4. Hedetniemi, Stephen T., Homomorphisms of graphs and automata (University of Michigan Technical Report, Project 03105–44-T, July, 1966; it is stated there that “the complete report is available in the major Navy technical libraries and can be obtained from the Defense Documentation Center“).Google Scholar
5. McAndrew, M. H., On the product of directed graphs, Proc. Amer. Math. Soc. 14 (1963), 600–606.Google Scholar
6. Sabidussi, G., Graph derivatives, Math. Z. 76 (1961), 385–401.Google Scholar
7. Sabidussi, G., Graph multiplication, Math. Z. 72 (1960), 446–457.Google Scholar
8. Weichsel, P. M., The Kronecker product of graphs, Proc. Amer. Math. Soc. 18 (1962), 47–52.Google Scholar