a. csaszar introduced and extensively studied the notionof generalized open sets. following csazar, we introduce a new notionsuperconnected. the main purpose of this paper is to study generalizedsuperconnected spaces. various characterizations of generalized super-connected spaces and preservation theorems are discussed.

A generalized p-cycle is a digraph whose set of vertices can be partitioned into p parts that are cyclically ordered in such a way that the vertices in one part are adjacent only to vertices in the next part. Any digraph can be shown as a p-cycle with p = 1, and bipartite digraphs are generalized p-cycles with p = 2. A maximally connected digraph is said to be superconnected if every disconnect...

We investigate the structure of a digraph having a transitive automorphism group where every cutset of minimal cardinality consists of all successors or all predecessors of some vertex. We improve most of the existing results in this area.

A non-cooperative model of network formation is developed. Link formation is one-sided. Information flow is two-way. The model builds on the work of Bala and Goyal who permit links to fail with a certain common probability. In our model the probability of failure can be different for different links. The set of networks which are Nash for suitably chosen model parameters consists of all essenti...

A Hausdorff topological space X is called superconnected (resp. coregular ) if for any nonempty open sets U 1 , … n ⊆ the intersection of their closures ‾ ∩ not empty complement ∖ ( a regular space). canonical example projective Q P ∞ vector < ω = { x ∈ : | ≠ 0 } over field rationals . The quotient by equivalence relation ∼ y iff ⋅ We prove that every countable second-countable homeomorphic to ...

The conditional diameter Dν of a digraph G measures how far apart a pair of vertex sets V1 and V2 can be in such a way that the minimum out-degree and the minimum in-degree of the subdigraphs induced by V1 and V2, respectively, are at least ν. Thus, D0 is the standard diameter and D0 ≥ D1 ≥ . . . ≥ Dδ, where δ is the minimum degree. We prove that if Dν ≤ 2` − 3, where ` is a parameter related t...