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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Enumerating $ 2$-cell imbeddings of connected graphs


Authors: Bruce P. Mull, Robert G. Rieper and Arthur T. White
Journal: Proc. Amer. Math. Soc. 103 (1988), 321-330
MSC: Primary 05C10; Secondary 05C30
MathSciNet review: 938690
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Abstract: A systematic approach is developed for enumerating congruence classes of $ 2$-cell imbeddings of connected graphs on closed orientable $ 2$-manifolds. The method is applied to the wheel graphs and to the complete graphs. Congruence class genus polynomials and congruence class imbedding polynomials are introduced, to summarize important information refining the enumeration.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0938690-1
PII: S 0002-9939(1988)0938690-1
Keywords: Topological graph theory, connected graph, closed orientable $ 2$-manifold, $ 2$-cell imbedding, congruent imbeddings, rotation, equivalent rotations, wheel graph, complete graph, congruence class genus polynomial, congruence class imbedding polynomial, graph automorphism, map automorphism
Article copyright: © Copyright 1988 American Mathematical Society