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Balanced sets and Q-polynomial association schemes. (English) Zbl 0644.05016
The author’s abstract: “The notion of a balanced set of vectors is defined, and the classification of such sets suggested. A slightly stronger condition is considered for association schemes, with the following result. Let X be a d-class symmetric association scheme with Bose-Mesner algebra M and Krein parameters \(q^ h_{ij}\), and let \(E=E_ t\) (0\(\leq t\leq d)\) be any primitive idempotent of M. For each \(x\in X\) let \(x_ E\) denote the diagonal matrix with y, y entry \(E_{xy}\) (y\(\in X)\). Define the representation diagram \(D_ E\) on the nodes 0,1,...,d by drawing an undi (1987).
A graph is said to be k-neighbour connected if the removal of \(t<k\) closed neighbourhoods result neither in a disconnected nor in a complete graph. The authors give the sharp lower bound on the number of vertices of k-regular, k-neighbour connected graph whose every 5-cycle belongs to a clique.
Reviewer: P.Horák

05B30 Other designs, configurations
05C40 Connectivity
Full Text: DOI
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