Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Factorizations of the complete graph into C-5-factors and 1-factors

In this paper, we show that K-10n can be factored into alpha C-5-factors and beta 1-factors for all non-negative integers alpha and beta satisfying 2alpha + beta = 10(n) - 1.

A graphical specification of model transformations with triple graph grammars

Models and model transformations are the core concepts of OMG's MDA (TM) approach. Within this approach, most models are derived from the MOF and have a graph-based nature. In contrast, most of the current model transformations are specified textually. To enable a graphical specification of model transformation rules, this paper proposes to use triple graph grammars as declarative specification formalism. These triple graph grammars can be specified within the FUJABA tool and we argue that these rules can be more easily specified and they become more understandable and maintainable. To show the practicability of our approach, we present how to generate Tefkat rules from triple graph grammar rules, which helps to integrate triple graph grammars with a state of a art model transformation tool and shows the expressiveness of the concept.