A concept of folding for compact connected surfaces, involving the partition of the surface into combinatorially identical n-sided topological polygons, is defined. The existence of such foldings for given n and given surfaces is explored, with definitive results for the sphere and the toms. We obtain necessary conditions for the existence of such foldings in all other cases.Mathematics Subject Classifications (1991): 57N05, 54C05.
ABSTRACT:In this paper we examined the relation between digraph folding of a given pair of digraphs and digraph folding of new digraphs generated from these given pair of digraphs by some known operations like union, intersection, joins, Cartesian product and composition. We first redefined these known operations for digraphs, then we defined some new maps of these digraphs and we called these maps union, intersection, join, Cartesian and composition dimaps. In each case we obtained the necessary and sufficient conditions, if exist,for a dimap to be digraph folding. Finally we explored the digraph folding, if there exist any, by using the adjacency matrices.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.