Closure operators associated with networks

Abstract

We study network (i.e., undirected simple graph) structures by investigating associated closure operators and the corresponding closed sets. To describe the dynamic behavior of networks, we employ continuous transformations and neighborhood homomorphisms between them. These transformations and homomorphisms are then studied. In particular, the problem of preserving generators by continuous transformations and that of preserving minimal dominating sets by neighborhood homomorphisms are dealt with.

Some Variants of Strong Normality in Closure Spaces Generated via Relations

“…ey proved that topology generated from aftersets and foresets is dual if the relation is preorder. ey also introduced lower separation axioms in terms of relation and studied these closure spaces in digital topology.Šlapal and Pfaltz [7] utilized binary relations in networks and studied closure operators associated with networks. B. M. R. Stadler and P. F. Stadler [8] studied some higher separation axioms in closure spaces, and recently, Gupta and Das [9] investigated variants of normality in closure setting by using cannonically closed sets.…”