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A definition of regularity was given in [2] for non-commutative graded algebras and the results of [2] together with those in [4, 5] classify the regular algebras of global dimension three that are generated by degree one elements. Our purpose is to classify a certain class of quadratic regular algebras of global dimension four. Let S be a twisted… (More)

We consider graded Clifford algebras on n generators in the spirit of Artin, Tate and Van den Bergh’s non-commutative algebraic geometry. We give an algorithm for counting the point modules over such an algebra, and prove that a generic graded Clifford algebra on four generators has defining relations which are determined by their zero locus in P × P.… (More)

New upper bounds for the independence number and for the clique covering number of a graph are given in terms of the rank, respectively the eigenvalues, of the adjacency matrix. We formulate a conjecture concerning an upper bound of the clique covering number. This upper bound is related to an old conjecture of Alan J. Hoffman which is shown to be false.

Upper bounds for the length of a longest (circuit) cycle without chords in a (directed) graph are given in terms of the rank of the adjacency matrix and in terms of its eigenvalues.

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