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 embeddin
New families of strongly regular graphs
β Scribed by Yury J. Ionin; Hadi Kharaghani
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 116 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1063-8539
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β¦ Synopsis
Abstract
We apply symmetric balanced generalized weighing matrices with zero diagonal to construct four parametrically new infinite families of strongly regular graphs. Β© 2003 Wiley Periodicals, Inc. J Combin Designs 11: 208β217, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10038
π SIMILAR VOLUMES
## Abstract It is shown that certain conditions assumed on a regular selfβcomplementary graph are not sufficient for the graph to be strongly regular, answering in the negative a question posed by Kotzig in [1].
It is well known that any finite simple graph Ξ is an induced subgraph of some exponentially larger strongly regular graph Ξ (e.g., [2,8]). No general polynomial-size construction has been known. For a given finite simple graph Ξ on v vertices, we present a construction of a strongly regular graph Ξ
By a square in an undirected graph β« , we mean a cycle x , y , z , w such that x is not adjacent to z and y is not adjacent to w . Suppose that β« is a strongly regular graph with Ο 2 , and assume that β« does not contain a square . Pick any vertex x of β« and let β« Π denote the induced subgraph on the