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On genus imbeddings of the tensor product of graphs

✍ Scribed by Abay-Asmerom, Ghidewon

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
566 KB
Volume
23
Category
Article
ISSN
0364-9024

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✦ Synopsis

In this article new genus results for the tensor product H @ G are presented. The second factor G in H @ G is a Cayley graph. The imbedding technique used to establish these results combines surgery and voltage graph theory. This technique was first used by A. T. White [171. This imbedding technique starts with a suitable imbedding of H on some surface and proceeds by modifying H according to the structure of G to give H * . The resulting pseudograph H* is a voltage graph whose covering graph is the tensor product H @ G. Using our knowledge of the order, size, and the number of regions in the imbedding of H * , together with the theory of voltage graphs, we are able to find the minimum genus of the imbedding surface for several families of the product H @ G.

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