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Embeddings of tensor product graphs. (English) Zbl 0848.05025
Alavi, Y. (ed.) et al., Graph theory, combinatorics, algorithms and applications. Vol. 2. Proceedings of the seventh quadrennial international conference on the theory and applications of graphs, Kalamazoo, MI, USA, June 1-5, 1992. New York, NY: Wiley. 893-904 (1995).
The paper surveys recent results and known methods for constructing embeddings of tensor product graphs in closed surfaces. In the tensor product $$G \otimes H$$ of two graphs $$G$$ and $$H$$, vertices are the ordered pairs of vertices of $$G$$ and $$H$$, respectively, and a vertex $$(u_1, u_2)$$ is adjacent to a vertex $$(v_1, v_2)$$ whenever $$u_1$$ is adjacent to $$v_1$$ and $$u_2$$ is adjacent to $$v_2$$. The embedding techniques considered in the paper are diagonalizable embeddings, angle valuations, map products, and voltage graph surgery. Special emphasis is put on the last topic.
For the entire collection see [Zbl 0839.00020].

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory
##### Keywords:
tensor product graphs; closed surfaces; embedding; voltage graph