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Regular Embeddings of Canonical Double Coverings of Graphs by Roman Nedela; Martin Škoviera is a Computer Science article available to read on EtoBox.

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This paper addresses the question of determining, for a given graph G, all regular maps having G as their underlying graph, i.e., all embeddings of G in closed surfaces exhibiting the highest possible symmetry. We show that if G satisfies certain natural conditions, then all orientable regular embeddings of its canonical double covering, isomorphic to the tensor product G K 2 , can be described in terms of regular embeddings of G. This allows us to ``lift'' the classification of regular embeddings of a given graph to a similar classification for its canonical double covering and to establish various properties of the ``derived'' maps by employing those of the ``base'' maps. We apply these results to determining all orientable regular embeddings of the tensor products K n K 2 (known as the cocktail-party graphs) and of the n-dipoles D n , the graphs consisting of two vertices and n parallel edges joining them. In the first case we show, in particular, that regular embeddings of K n K 2 exist only if n is a prime power p l , and there are 2,(n&1) or ,(n&1) isomorphism classes of such maps (where , is Euler's function) according to whether l is even or odd. For l even an interesting n

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Author

Roman Nedela; Martin Škoviera

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0095-8956)

Published

1996

Language

EN

Field

Computer Science (Physical Sciences)