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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

##### MSC:
 05B30 Other designs, configurations 05C40 Connectivity
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##### References:
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