Let denote a bipartite distance-regular graph with diameter D β₯ 4 and valency k β₯ 3. Let ΞΈ 0 > ΞΈ 1 > β’ β’ β’ > ΞΈ D denote the eigenvalues of and let E 0 , E 1 , . . . , E D denote the associated primitive idempotents. Fix s (1 β€ s β€ D -1) and abbreviate E := E s . We say E is a tail whenever the entry
Distance Biregular Bipartite Graphs
β Scribed by C. Delorme
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 392 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0195-6698
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β¦ Synopsis
We describe here some properties of a class of graphs which extends the class of distance regular graphs: our graphs are bipartite and for cach vertex there exists an intersection array depending on the stable component of the vertex. Thus our graphs arc to distance regular graphs as bipartite regular graphs are to regular graphs. They also are to non-symmetric association schemes as distance regular graphs are to symmetric association schemes. We also give some examples.
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