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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.

05C12 Distance in graphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05E30 Association schemes, strongly regular graphs
Full Text: DOI
[1] Bannai, E.; Ito, T., Algebraic combinatorics I: association schemes, (1984), Benjamin, Cummings London · Zbl 0555.05019
[2] Brouwer, A.E.; Cohen, A.M.; Neumaier, A., Distance-regular graphs, (1989), Springer Berlin · Zbl 0747.05073
[3] Curtin, B., 2-homogeneous bipartite distance-regular graphs, Discrete math., 187, 39-70, (1998) · Zbl 0958.05143
[4] Godsil, C.D., Algebraic combinatorics, (1993), Chapman and Hall, Inc. New York · Zbl 0814.05075
[5] Jurišić, A.; Koolen, J.; Terwilliger, P., Tight distance-regular graphs, J. algebraic combin., 12, 163-197, (2000) · Zbl 0959.05121
[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
[8] MacLean, M.; Terwilliger, P., Taut distance-regular graphs and the subconstituent algebra, Discrete math., 306, 1694-1721, (2006) · Zbl 1100.05104
[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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