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Metrically regular square of metrically regular bipartite graphs of diameter \(D=6\). (English) Zbl 0797.05060

Summary: The paper deals with the spectra of powers of metrically regular graphs. We prove that there is only one table of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter \(D=6\) (7 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter \(D<6\), see [the author, ibid. 27b, 183-197 (1991; Zbl 0764.05068)] and [the author, ibid. 28, No. 1-2, 17-24 (1992; Zbl 0778.05058)].

MSC:

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