Abstract. In the context of DNA computing, an operation on words, called splicing, was introduced by Head (1987), in his study on recombinant behavior of DNA molecules. Recently, a special kind of splicing, called flat splicing on strings, was considered and several properties were derived. On the other hand, in the study of modelling of distributed complex systems based on language theory, grammar systems were proposed. Here we introduce a grammar system, called alphabetic flat splicing pure context-free grammar system ,)ܵܩܨܥܲܵܨܣ( as a new model of language generation, based on the operation of alphabetic flat splicing on words and pure context-free rules. We derive certain comparison results that bring out the generative power of ܵܩܨܥܲܵܨܣ and as an application construct a ܵܩܨܥܲܵܨܣ generating "floor-design" pictures.
An assignment of labels (mostly, integers) to the vertices of a graph G(V,E), or simply G, on n vertices subject to certain constraints is called a vertex labeling of G. A graph G is a divisor graph if the vertices of G can be labeled with integers (necessarily distinct) in such a way that either x|y or y|x for any two adjacent vertices x and y. In this paper, we encounter the divisor labeling of certain classes of graphs.
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