AUTHOR(S):

TITLE Structuring Digital Plane by the 8Adjacency Graph with a Set of Walks 
ABSTRACT In the digital plane Z2, we define connectedness induced by a set of walks of the same lengths in the 8adjacency graph. The connectedness is shown to satisfy a digital analogue of the Jordan curve theorem. This proves that the 8adjacency graph with a set of walks of the same lengths provides a convenient structure on the digital plane Z2 for the study of digital images.

KEYWORDS Digital plane, 8adjacency graph, walk, connectedness, Jordan curve theorem

REFERENCES [1] F. Harrary, Graph Theory, AddisonWesley Publ. Comp., Reading, Massachussets–Menlo Park, California–London–Don Mills, Ontario 1969. 
Cite this paper Josef Slapal. (2017) Structuring Digital Plane by the 8Adjacency Graph with a Set of Walks. International Journal of Mathematical and Computational Methods, 2, 150154 
