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arXiv · 1212.5752

Lifting Constructions of Strongly Regular Cayley Graphs

Koji Momihara·Qing Xiang
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Abstract

We give two "lifting" constructions of strongly regular Cayley graphs. In the first construction we "lift" a cyclotomic strongly regular graph by using a subdifference set of the Singer difference set. The second construction uses quadratic forms over finite fields and it is a common generalization of the construction of the affine polar graphs \cite{CK86} and a construction of strongly regular Cayley graphs given in \cite{FWXY}. The two constructions are related in the following way: The second construction can be viewed as a recursive construction, and the strongly regular Cayley graphs obtained from the first construction can serve as starters for the second construction. We also obtain association schemes from the second construction.

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Koji Momihara, Qing Xiang. 2012-12-23. Lifting Constructions of Strongly Regular Cayley Graphs. https://arxiv.org/abs/1212.5752

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