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On soluble groups of automorphisms of nonorientable Klein surfaces

100%

Gromadzki G.

Fundamenta Mathematicae

1992

tom 141

nr 3

215-227

We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.

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Tree-like isometric subgraphs of hypercubes

63%

Brešar B., Imrich W., Klavžar S.

Discussiones Mathematicae Graph Theory

2003

tom 23

nr 2

227-240

Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a generalization of median graphs. Just as median graphs they capture numerous properties of trees, but may contain larger classes of graphs that may be easier to recognize than the class of median graphs. We investigate the structure of tree-like partial cubes, characterize them, and provide examples of similarities with trees and median graphs. For instance, we show that the cube graph of a tree-like partial cube is dismantlable. This in particular implies that every tree-like partial cube G contains a cube that is invariant under every automorphism of G. We also show that weak retractions preserve tree-like partial cubes, which in turn implies that every contraction of a tree-like partial cube fixes a cube. The paper ends with several Frucht-type results and a list of open problems.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Fundamenta Mathematicae

1 Brešar B.

1 Gromadzki G.

1 Imrich W.

1 Klavžar S.

1 2003

1 1992

Wyniki wyszukiwania

On soluble groups of automorphisms of nonorientable Klein surfaces

Tree-like isometric subgraphs of hypercubes