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Families of Regular Graphs in Regular Maps

✍ Scribed by Steve Wilson

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 227 KB
Volume: 85
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2103

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✦ Synopsis

The question of when a given graph can be the underlying graph of a regular map has roots a hundred years old and is currently the object of several threads of research. This paper outlines this topic briefly and proves that a product of graphs which have regular embeddings also has such an embedding. We then present constructions for members of three families: (1) circulant graphs, (2) wreath graphs W(k, n), whose vertices are ordered pairs (i, j), 0 [ i < k, 0 [ j < n, and whose edges are all possible (i, j) -(i+1, jOE), and (3) depleted wreath DW(k, n), the subgraph of W(k, n) left by removing all edges in which j=jOE. We open the question of multiplicity of occurrence and we list the underlying graphs of rotary maps with no more than 50 edges.

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