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A characterization of distance-regular graphs with diameter three. (English) Zbl 0874.05060

Summary: We characterize the distance-regular graphs with diameter three by giving an expression for the number of vertices at distance two from each given vertex, in terms of the spectrum of the graph.

MSC:

05E30 Association schemes, strongly regular graphs
05C75 Structural characterization of families of graphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C12 Distance in graphs
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References:

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