On the weak distance-regularity of Moore-type digraphs

We prove that Moore digraphs, and some other classes of extremal digraphs, are weakly distance-regular in the sense that there is an invariance of the number of walks between vertices at a given distance. As weakly distance-regular digraphs, we then compute their complete spectrum from a 'small...

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Bibliographic Details
Published in:Linear & multilinear algebra 2006-07, Vol.54 (4), p.265-284
Main Authors: Comellas, F., Fiol, M. A., Gimbert, J., Mitjana, M.
Format: Article
Language:English
Subjects:
Adjacency spectrum
AMS Subject Classifications: 05C50
Line digraph
Moore digraphs
Weakly distance-regular digraph
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Summary:We prove that Moore digraphs, and some other classes of extremal digraphs, are weakly distance-regular in the sense that there is an invariance of the number of walks between vertices at a given distance. As weakly distance-regular digraphs, we then compute their complete spectrum from a 'small' intersection matrix. This is a very useful tool for deriving some results about their existence and/or their structural properties. For instance, we present here an alternative and unified proof of the existence results on Moore digraphs, Moore bipartite digraphs and, more generally, Moore generalized p-cycles. In addition, we show that the line digraph structure appears as a characteristic property of any Moore generalized p-cycle of diameter D ≥ 2p.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081080500423825