Showing papers by "Matej Bel University published in 2002"
TL;DR: It is proved that for any prime number p the complete bipartite graph K p , p has, up to isomorphism, precisely one regular embedding on an orientable surface—the well-known embedding with faces bounded by hamiltonian cycles.
36 citations
TL;DR: In this paper, it was shown that in a finite 1/2-transitive graph of valency 4 and girth 4, the set of 4-cycles decomposes the edge set in such a way that either every 4-cycle is alternating or every 4cycle is directed relative to this orientation.
Abstract: Finite graphs of valency 4 and girth 4 admitting 1/2-transitive group actions, that is, vertex- and edge- but not arc-transitive group actions, are investigated. A graph is said to be 1/2- transitive if its automorphism group acts 1/2-transitively. There is a natural orientation of the edge set of a 1/2-transitive graph induced and preserved by its automorphism group. It is proved that in a finite 1/2-transitive graph of valency 4 and girth 4 the set of 4-cycles decomposes the edge set in such a way that either every 4-cycle is alternating or every 4-cycle is directed relative to this orientation. In the latter case vertex stabilizers are isomorphic to 2.
26 citations
TL;DR: Regular homomorphisms of oriented maps essentially arise from a factorization by a subgroup of automorphisms, and are generalized to the case when the induced homomorphism of the underlying graphs is not valency preserving.
Abstract: Regular homomorphisms of oriented maps essentially arise from a factorization by a subgroup of automorphisms. This kind of map homomorphism is studied in detail, and generalized to the case when the induced homomorphism of the underlying graphs is not valency preserving. Reconstruction is treated by means of voltage assignments on angles, a natural extension of the common assignments on darts. Lifting and projecting groups of automorphisms along regular homomorphisms is studied in some detail. Finally, the split-extension structure of lifted groups is analysed.
20 citations
18 Aug 2002
TL;DR: The paper presents a possibility of exploitation of distributed genetic algorithms (DGAs) for optimization of the neural networks and fuzzy neural networks (FNNs) structure and its application to pattern recognition.
Abstract: The paper presents a possibility of exploitation of distributed genetic algorithms (DGAs) for optimization of the neural networks (NNs) and fuzzy neural networks (FNNs) structure and its application to pattern recognition. Generally, there can be several approaches to generation structure of NNs based on genetic algorithms (GAs). Two of them are used most frequently. In the first approach, NNs are only generated from a genotype while in the second approach two genotypes are used. These methods make use of GAs to determine: synapse weights NNs, where their structure is known in advance; NNs structure and synapse weights. This proposal belongs to the second group of methods. These make use of GAs to determine structure and synapse weights NNs (FNNs).
2 citations