Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-19T10:52:03.575Z Has data issue: false hasContentIssue false

On the Genus of Strong Tensor Products of Graphs

Published online by Cambridge University Press:  20 November 2018

B. L. Garman
Affiliation:
Western Michigan University, Kalamazoo, Michigan 49008
R. D. Ringeisen
Affiliation:
Western Michigan University, Kalamazoo, Michigan 49008
A. T. White
Affiliation:
Purdue University, Fort Wayne, Indiana 46805
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The genus parameter for graphs has been studied extensively in recent years, with impetus given primarily by the Ringel-Youngs solution to the Heawood Map-coloring Problem [15]. This solution involved the determination of 𝛄(Kn), the genus of the complete graph Kn.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Battle, J., Harary, F., Kodama, Y., and Youngs, J. W. T., Additivity of the genus of a graph, Bull. Amer. Math. Soc. 68 (1962), 565568.Google Scholar
2. Behzad, M. and Chartrand, G., An introduction to the theory of graphs (Allyn and Bacon, Boston, 1971).Google Scholar
3. Cairns, E. S., Introductory topology (Ronald Press, New York, 1968).Google Scholar
4. Garman, B., On the genus of Knin, Notices Amer. Math. Soc. 20 (1973), A-564.Google Scholar
5. Garman, B., Imbedding Cayley graphs, Specialist thesis, Western Michigan University, 1974.Google Scholar
6. Gross, J. L., Voltage graphs, Discrete Math. 9 (1974), 239246.Google Scholar
7. Gross, J. L. and Alpert, S. R., Branched coverings of current graph imbeddings, Bull. Amer. Math. Soc. 79 (1973), 942945.Google Scholar
8. Gustin, W., Orientable embedding of Cayley graphs, Bull. Amer. Math. Soc. 69 (1963), 272275.Google Scholar
9. Harary, F., Graph theory (Addison-Wesley, Reading, Mass., 1969).Google Scholar
10. Harary, F. and Wilcox, G., B∞lean operations on graphs, Math. Scand. 20 (1967), 4151.Google Scholar
11. Jungerman, M., The genus of the symmetric quadripartite graph, J. Combinatorial Theory B19 (1975), 181187.Google Scholar
12. Kronk, H. V., Ringeisen, R. D., and White, A. T., On 2-cell imbeddings of complete n-partite graphs, to appear, Colloq. Math.Google Scholar
13. Ringel, G., Genus of graphs, Combinatorial Structures and their Applications, Guy, R., Hanani, H., Sauer, N., and Schonheim, J., editors (Gordon and Breach, New York, 1970), 361366.Google Scholar
14. Ringel, G., Map color theorem (Springer-Verlag, Berlin, 1974).Google Scholar
15. Ringel, G. and Youngs, J. W. T., Solution of the Heaw∞d map-coloring problem, Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 438445.Google Scholar
16. Ringel, G. and Youngs, J. W. T., Das Geschlecht des symmetrische vollstandige dreifarbaren Graphen, Comment. Math. Helv. 45 (1970), 152158.Google Scholar
17. Sabidussi, G., Graph multiplication, Math. Z. 72 (1960), 446457.Google Scholar
18. Weichsel, P. M., The Kronecker product of graphs, Proc. Amer. Math. Soc. 13 (1963), 4752.Google Scholar
19. White, A. T., The genus of the complete tripartite graph Kmninin, J. Combinatorial Theory 7 (1969), 283285.Google Scholar
20. White, A. T., The genus of repeated cartesian products of bipartite graphs, Trans. Amer. Math. Soc. 151 (1970), 393404.Google Scholar
21. White, A. T., On the genus of the composition of two graphs, Pacific J. Math. 1+1 (1972), 275279.Google Scholar
22. White, A. T., The genus of cartesian products of graphs, Ph.D. Thesis, Michigan State University, 1969.Google Scholar
23. White, A. T., Graphs, groups, and surfaces (North-Holland, Amsterdam, 1973).Google Scholar
24. White, A. T., Orientable imbeddings of Cayley graphs, Duke Math. J. 41 (1974), 353371.Google Scholar
25. Wilson, R., Introduction to graph theory (Academic Press, New York and London, 1972).Google Scholar