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A new approach to the bipartite fundamental bound. (English) Zbl 1254.05054

The author defined taut graphs as bipartite distance regular graphs that satisfy an inequality proved in [M. S. MacLean, Discrete Math 225, No. 1–3, 193–216 (2000; Zbl 1001.05124)]. Here the author gives a new linear-algebraic characterization of taut graphs.

MSC:

05C12 Distance in graphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05E30 Association schemes, strongly regular graphs

Citations:

Zbl 1001.05124
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Full Text: DOI

References:

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[6] MacLean, M., An inequality involving two eigenvalues of a bipartite distance-regular graph, Discrete Math., 225, 193-216 (2000) · Zbl 1001.05124
[7] MacLean, M., Taut distance-regular graphs of odd diameter, J. Algebraic Combin., 17, 125-147 (2003) · Zbl 1014.05072
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[9] MacLean, M.; Terwilliger, P., The subconstituent algebra of a bipartite distance-regular graph: thin modules with endpoint two, Discrete Math., 308, 1230-1259 (2008) · Zbl 1136.05076
[10] Nomura, K., Homogeneous graphs and regular near polygons, J. Combin. Theory Ser. B, 60, 63-71 (1994) · Zbl 0793.05130
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