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The Maximum Genus of Cartesian Products of Graphs

Published online by Cambridge University Press:  20 November 2018

Joseph Zaks
Joseph Zaks*
Affiliation:
Michigan State University, East Lansing, Michigan; University of Haifa, Haifa, Israel
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1025 - 1035
Copyright
Copyright © Canadian Mathematical Society 1974

References

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