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In this paper, our main goal is to investigate chromaticity of the general multipartite graphs. A method to find chromatically unique multipartite graphs is obtained. By the method, we give some chromatically unique multipartite graphs.
Various aspects of combinatorial information concerning a graph is stored in the coefficients of a specific graph polynomial, so represented also by the roots of such graph polynomial. It is natural to ask about the nature and location of the roots. In this paper, the orderings of some graphs by the minimum real roots of their adjoint polynomials are obtained. Moreover, the orderings of some trees...
In this paper we discuss the relation between the number restriction and existential restriction in description logic ALepsivN. We show that incompatible existential restrictions on the top conjunction of concept descriptions can deduce a number restriction, exactly speaking an at least restriction. Firstly we define the incompatible relation among the existential restrictions on the top conjunction...
A polynomial time isomorphism test for a class of groups, properly containing the class of abelian groups, is presented. Isomorphism testing of group presentations for (a subclass of) the same class of groups is shown to be (graph) isomorphism complete. These seem to be the first known isomorphism complete problems in group theory. Subexponential tests are presented as well for rings and algebras.
An O(n2) space representation for permutation groups of degree n is presented. The representation can be constructed in time O(n5), and supports fast membership testing. Applications of the representation to the generation of systems of coset representatives, and of complete block systems, are discussed.
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