Sungpyo Hong

Regular graph coverings whose covering transformation groups have the isomorphism extension property

Abstract Enumerative results are presently a major center of interest in topological graph theory, as in the work of Gross and Furst [1], Hofmeister [5,6], Kwak and Lee [9–13] and Mull et al. [15], etc. Kwak and Lee [9] enumerated the isomorphism classes of graph bundles and those of n -fold graph coverings with respect to a group of automorphisms of the base graph which fix a spanning tree. Hofmeister [6] enumerated independently the isomorphism classes of n -fold graph coverings with respect to the trivial automorphism group of the base graph. But the enumeration of isomorphism classes of regular graph coverings has not been answered completely. As its partial answers, Hofmeister enumerated the isomorphism classes of Z 2 -coverings (double coverings) with respect to any group of automorphisms of the base graph, and Sato [14] did the same work for Z p -coverings (regular prime-fold coverings). With respect to the trivial automorphism group of the base graph, Hong and Kwak [8] did the same work for Z 2 ⊕ Z 2 or Z 4 -coverings, and Kwak and Lee [10] did it for Z p , Z p ⊕ Z 1 ( p ≠ q primes) or Z p 2 -coverings. As an expansion of this effort, we obtain in this paper several new algebraic characterizations for isomorphic regular coverings and derive an enumerating formula for the isomorphism classes of A-coverings of a graph G with respect to any group of automorphisms of G which fix a spanning tree, when the covering transformation group A has the isomorphism extension property. By definition, it means that every isomorphism between any two isomorphic subgroups B 1 and B 2 of A can be extended to an automorphism of A. Also, we obtain complete numerical enumeration of the isomorphism classes of Z n -coverings for all n , D n -coverings for odd n (D n is the dihedral group of order 2 n ) or Z p ⊕ Z p -coverings of a graph G for prime p with respect to the trivial automorphism group of G . In addition, we applied our results to a bouquet of circles.

Geometric inequalities for spacelike hypersurfaces in the Minkowski spacetime

Abstract We derive a linear isoperimetric inequality and some geometric inequalities for properly located compact achronal spacelike hypersurfaces via a Minkowski-type integral formula in the Minkowski spacetime.

Isoperimetric inequalities for sectors in the Minkowski 2-spacetime

AbstractIn the Minkowski 2-spacetime

Bipartite graph bundles with connected fibres

\mathbb{L}^2

Linear Equations and Matrices

the hyperbolic angle is defined by the hyperbolic parametrization of the plane. With this notion of hyperbolic angle Helzer obtained a relativistic version of Gauss-Bonnet formula (cf. [3]). In this paper, we derive an isoperimetric inequality for timelike sectors in

Inner Product Spaces

\mathbb{L}^2