# zbMATH — the first resource for mathematics

Generalization of Železník’s theorem on embeddings of tensor products of graphs. (English) Zbl 0853.05031
Summary: If a simple graph $$G$$ has a diagonalizable quadrilateral embedding, then given an arbitrary simple graph $$H$$, the tensor product $$G \otimes H$$ also has a diagonalizable quadrilateral embedding. Using a (generalized) rotation scheme for a diagonalizable quadrilateral embedding of the graph $$G$$ and a rotation scheme for an embedding of the graph $$H$$, a (generalized) rotation scheme which determines a diagonalizable quadrilateral embedding of $$G \otimes H$$ is constructed.

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory
Full Text:
##### References:
 [1] ABAY-ASMEROM G.: On genus embedding of the tensor product of graphs. · Zbl 0860.05025 [2] Beineke L.-Wilson R. J. (eds.): Selected Topics in Graph Theory. Academic Press, New York, 1978. · Zbl 0423.00003 [3] BOUCHET A.: Produit tensoriel de rotations. Journées de Combinatoire et Informatique de Bordeaux, Editions Univ. Bordeaux 1 (1975), 53-59. · Zbl 0344.05163 [4] BOUCHET A.-MOHAR B.: Triangular embeddings of tensor products of graphs. Topics in Combinatorics and Graph Theory (R. Bodendiek and R. Henn, Physica-Verlag, Heidelberg, 1990, pp. 129-135. · Zbl 0697.05025 [5] DAKIĆ T.-PISANSKI T.: On the genus of the tensor product of graphs where one factor is a regular graph. Discrete Math. · Zbl 0812.05019 [6] DAKIĆ T.-NEDELA R.-PISANSKI T.: Embeddings of tensor product graphs. Proc. of the Seventh Conference on Graph Theory, Combinatorics, Algorithms and Applications, Kalamazoo · Zbl 0848.05025 [7] GROSS J. L.-TUCKER T. W.: Topological Graph Theory. John Wiley & Sons, New York, 1987. · Zbl 0621.05013 [8] HARARY F.-WILCOX G. W.: Boolean operations on graphs. Math. Scand. 20 (1967), 41-51. · Zbl 0152.22801 [9] WEICHSEL P. M.: The Kronecker product of graphs. Proc. Amer. Math. Soc. 13 (1962), 47-52. · Zbl 0102.38801 [10] WHITE A. T.: Covering graphs and graphical products. Proc. Sixth Yugoslav Seminar of Graph Theory (Dubrovnik 1985), Novi Sad, 1986, pp. 239-247. [11] WHITE A. T.: Graphs, Groups and Surfaces. (2nd Edition), North-Holland, Amsterdam. · Zbl 0268.05102 [12] ŽELEZNÍK V.: Quadrilateral embeddings of the conjunction of graphs. Math. Slovaca 38 (1988), 89-98. · Zbl 0654.05025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.