Geodesic
The Maximum Genus of Cartesian Products of Graphs
Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1025-1035

Voir la notice de l'article provenant de la source Cambridge University Press

The maximum genus γM(G) of a connected graph G has been defined in [2] as the maximum g for which there exists an embedding h : G —> S(g), where S(g) is a compact orientable 2-manifold of genus g, such that each one of the connected components of S(g) — h(G) is homeomorphic to an open disk; such an embedding is called cellular. If G is cellularly embedded in S(g), having V vertices, E edges and F faces, then by Euler's formula V-E + F = 2-2g. 
Zaks, Joseph. The Maximum Genus of Cartesian Products of Graphs. Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1025-1035. doi: 10.4153/CJM-1974-096-2
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[1] 1. Duke, R., The genus, regional number, and the Betti number of a graph, Can. J. Math. 18 (1966), 817–822. Google Scholar

[2] 2. Nordhaus, E. A., Stewart, B. M., and White, A. T., On the maximum genus of a graph, J. Combinatorial Theory Ser. B 11 (1971), 258–267. Google Scholar

[3] 3. Nordhaus, E. A., Ringeisen, R. D., Stewart, B. M., and White, A. T., A Kuratowski-type theorem for the maximum genus of a graph, J. Combinatorial Theory Ser. B 12 (1972), 260–267. Google Scholar

[4] 4. Ringeisen, R. D., Determining all compact orientable 2-manifolds upon which Kmtn has 2-cell imbeddings, J. Combinatorial Theory Ser. B 12 (1972) 101–104. Google Scholar

[5] 5. Ringeisen, R. D., Upper and lower imbeddable graphs, Graph theory and applications (Y. Alavi, et al.» editors), Springer-Verlag, Vol. 303, 1972 6. G. Sabidussi, Graph multiplication, Math. Z. 72 (1960), 446–457. Google Scholar

[7] 7. Tutte, W. T., The factorization of linear graphs, J. London Math. Soc. 22 (1947), 107–111. Google Scholar

[8] 8. White, A. T., The genus of the Cartesian product of two graphs, J. Combinatorial Theory Ser. B 11 (1971), 89–94. Google Scholar

[9] 9. White, A. T., On the genus of products of graphs, Recent Trends in Graph Theory (M. Capobianco, et al., editors), Springer-Verlag, Vol. 186, 1971. Google Scholar

[10] 10. Zaks, J., On the 1-factors of n-connected graphs, J. Combinatorial Theory Ser. B 11 (1971), 169–180. Google Scholar

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