a parallel algorithm for generating t-ary tree sequences in reverse b-order is presented. the algorithm generates t-ary trees by 0-1 sequences, and each 0-1 sequences is generated in constant average time o(1). the algorithm is executed on a crew sm simd model, and is adaptive and cost-optimal. prior to the discussion of the parallel algorithm a new sequential generation with o(1) average time ...

For every pair of nite connected graphs F and H, and every integer k, we construct a universal graph U with the following properties: 1. There is a homomorphism : U ! H, but no homomorphism from F to U . 2. For every graph G with maximal degree no more than k having a homomorphism h : G! H, but no homomorphism from F to G, there is a homomorphism : G! U , such that h = . Particularly, this solv...

The chromatic sum Σ(G) of a graph G is the smallest sum of colors among of proper coloring with the natural number. In this paper, we introduce a necessary condition for the existence of graph homomorphisms. Also, we present Σ(G) < χf (G)|G| for every graph G.

We consider the complexity of oriented homomorphism and two of its variants, namely strong oriented homomorphism and pushable homomorphism, for planar graphs with large girth. In each case, we consider the smallest target graph such that the corresponding homomorphism is NP-complete. These target graphs T4, T5, and T6 have 4, 5, and 6 vertices, respectively. For i ∈ {4, 5, 6} and for every g, w...

We classify a type of language called a reflectable language. We then develop a generic algorithm that can be used to list all strings of length n for any reflectable language in Gray code order. The algorithm generalizes Gray code algorithms developed independently for k-ary strings, restricted growth strings, and k-ary trees, as each of these objects can be represented by a reflectable langua...

In this paper, we suggest a new technique to create index helping for querying almost identical similarities with keywords in case there is no correct match found. It’s based on a signature graph and n-ary tree helping to query related information when there is no correct match. Main idea is a signature graph structure, created based on signature file, created for a layer and signature files ar...

In this paper, we introduce the concept of fuzzy congruences on n-ary semigroups and describe quotient n-ary semigroups by fuzzy congruences. Some isomorphism theorems about n-ary semigroups are established. Moreover, we discuss a special kind of n-ary semigroups. We also establish relationships between normal fuzzy ideals and fuzzy congruences. In particular, we prove that there exists a prese...