Constructing isospectral non-isomorphic digraphs from hypergraphs
✍ Scribed by Barry Balof; Christopher Storm
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 124 KB
- Volume
- 63
- Category
- Article
- ISSN
- 0364-9024
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✦ Synopsis
Abstract
We explore the “oriented line graph” construction associated with a hypergraph, leading to a construction of pairs of strongly connected directed graphs whose adjacency operators have the same spectra. We give conditions on a hypergraph so that a hypergraph and its dual give rise to isospectral, but non‐isomorphic, directed graphs. The proof of isospectrality comes from an argument centered around hypergraph zeta functions as defined by Storm. To prove non‐isomorphism, we establish a Whitney‐type result by showing that the oriented line graphs are isomorphic if and only if the hypergraphs are. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 231–242, 2010