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2012

On distance-regular Cayley graphs on abelian groups

Miklavic, Stefko, Sparl, Primoz

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Let $G$ denote a finite abelian group with identity 1 and let $S$ denote an inverse-closed subset of $G \setminus {1}$, which generates $G$ and for which there exists $s \in S$, such that $\la S \setminus \{s,s^{-1}\} \ra \ne G$.

In this paper we obtain the complete classification of distance-regular Cayley graphs $\cay(G;S)$ for such pairs of $G$ and $S$.

On distance-regular Cayley graphs on abelian groups · Around

Built on

S. S. Shrikhande, The uniqueness of the
1959
Earlier work this paper cites.
W. G. Bridges and R. A. Mena, Rational circulants with rational spectra and cyclic strongly regular graphs,
1979
Earlier work this paper cites.
S. L. Ma, Partial Difference Sets,
1984
Earlier work this paper cites.

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D. Marušič, Strong regularity and circulant graphs,
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S. L. Ma, A Survey of Partial Difference Sets,
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A. E. Brouwer, A. M. Cohen and A. Neumaier,
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Then

Š. Miklavič and P. Potočnik, Distance-regular circulants,
2003
Later among the works it cites.
M. Muzychuk, Strongly regular Cayley graphs over the group
2005
Later among the works it cites.
Š. Miklavič and P. Potočnik, Distance-regular Cayley graphs on dihedral groups,
2007
Later among the works it cites.

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