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On pseudo-distance-regularity. (English) Zbl 0978.05050

The author uses (cosines of the) angles between eigenspaces of (the adjacency matrix of) a graph \(G\) on \(n\) vertices and the \(i\)th axis of a standard basis of \(\mathbb{R}^n\) (cf., e.g., the book by the reviewer, P. Rowlinson and S. Simić [Eigenspaces of graphs (Encyclopedia of Mathematics and Its Applications 66. Cambridge: Cambridge University Press) (1997; Zbl 0878.05057)]) and calls them the \(i\)-local multiplicities of the eigenvalues of \(G\). On this basis, in a previous paper by the author, E. Garriga and J. L. A. Yebra [J. Comb. Theory, Ser. B 68, No. 2, 179-205 (1996; Zbl 0861.05064)] the concept of local pseudo-distance regularity of a graph has been introduced. In the paper under review the author studies some properties of locally distance-regular graphs.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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