<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces satisfying a radius 2 local isomorphism (Boxer and Karaca, 2008; Han, 2006b; 2008b; 2008d; 2009b). However, for a digital covering which does not satisfy a radius 2 local isomorphism, the study of a digital fundamental group of a digital space and its automorphism group remains open. In order to examine this problem, the present paper establishes the notion of an ultra regular covering space, studies its various properties and calculates an automorphism group of the ultra regular covering space. In particular, the paper develops the notion of compatible adjacency of a digital wedge. By comparing an ultra regular covering space with a regular covering space, we can propose strong merits of the former.</p></abstract>

In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces satisfying a radius 2 local isomorphism (Boxer and Karaca, 2008; Han, 2006b; 2008b; 2008d; 2009b). However, for a digital covering which does not satisfy a radius 2 local isomorphism, the study of a digital fundamental group of a digital space and its automorphism group remains open. In order to examine this problem, the present paper establishes the notion of an ultra regular covering space, studies its various properties and calculates an automorphism group of the ultra regular covering space. In particular, the paper develops the notion of compatible adjacency of a digital wedge. By comparing an ultra regular covering space with a regular covering space, we can propose strong merits of the former.

Ultra regular covering space and its automorphism group

Institute of Pure and Applied Mathematics, Faculty of Liberal Education, Chonbuk National University, Jeonju-City Jeonbuk, 561-756, South Korea

International Journal of Applied Mathematics and Computer Science

{"article-title":"Ultra regular covering space and its automorphism group"}

In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca...

Ultra regular covering space and its automorphism group

Published Online: Dec 20, 2010

Page range: 699 - 710

DOI: https://doi.org/10.2478/v10006-010-0053-z

Keywords
digital image, digital isomorphism, (ultra) regular covering space, digital covering space, simply -connected, Deck's discrete transformation group, compatible adjacency, digital wedge, automorphism group

This content is open access.

Ultra regular covering space and its automorphism group

Published Online: Dec 20, 2010

Page range: 699 - 710

DOI: https://doi.org/10.2478/v10006-010-0053-z

Keywordsdigital image, digital isomorphism, (ultra) regular covering space, digital covering space, simply -connected, Deck's discrete transformation group, compatible adjacency, digital wedge, automorphism group

This content is open access.

Keywords
digital image, digital isomorphism, (ultra) regular covering space, digital covering space, simply -connected, Deck's discrete transformation group, compatible adjacency, digital wedge, automorphism group