A maximally connected digraph is said to be superconnected if every minimum disconnecting set F of vertices is trivial, i.e., it consists of the vertices adjacent to or from a given vertex not belonging to F . In this work, it is shown that a digraph is maximally connected provided that a certain condition on the diameter holds, and superconnected under a more restrictive constraint. These cond...

A graph is said to be edge-superconnected if each minimum edge-cut consists of all the edges incident with some vertex of minimum degree. A graph G is said to be a {d, d + 1}semiregular graph if all its vertices have degree either d or d+1. A smallest {d, d+1}-semiregular graph G with girth g is said to be a ({d, d+1}; g)-cage. We show that every ({d, d+1}; g)-cage with odd girth g is edge-supe...

A (k, g)-cage is a k-regular graph with girth g that has the fewest number of vertices. It has been conjectured [Fu, Huang, and Rodger, Connectivity of cages, J. Graph Theory 24 (1997), 187-191] that all (k, g)-cages are k-connected for k ≥ 3. A connected graph G is said to be superconnected if every minimum cut-set S is the neighborhood of a vertex of minimum degree. Moreover, if G − S has pre...

A. Csaszar introduced and extensively studied the notion of generalized open sets. Following Csazar, we introduce a new notion superconnected. The main purpose of this paper is to study generalized superconnected spaces. Various characterizations of generalized superconnected spaces and preservation theorems are discussed.

A maximally connected digraph is said to be superconnected if every minimum disconnecting set F of vertices is trivial, i.e., it consists of the vertices adjacent to or from a given vertex not belonging to F . This work is devoted to presenting a sufficient condition — in terms of the so called parameter ` — on the diameter, in order to guarantee that the digraph is superconnected, giving also ...

A k-container C(u, v) of a graph G is a set of k-disjoint paths joining u to v. A k-container C(u, v) of G is a k-container if it contains all the vertices of G. A graph G is k-connected if there exists a k-container between any two distinct vertices in G. Let κ(G) be the connectivity of G. A graph G is superconnected if G is i-connected for all 1 ≤ i ≤ κ(G). The pyramid network is one of the i...

In this paper we study the classes of superconnected and superfaithful left quasigroups, that are relevant in Mal’cev varieties quasigroups. Then focus on quandles particular to involutory ones. We extend main result [a by Erofeeva] infinite case offer a characterization several terms properties canonical generators displacement group, improving results Nobusawa].

A graph is superconnected, for short super-κ, if all minimum vertex-cuts consist of the vertices adjacent with one vertex. In this paper we prove for any r-regular graph of diameter D and odd girth g that if D ≤ g − 2, then the graph is super-κ when g ≥ 5 and a complete graph otherwise.

Interconnection networks form an important area which has received much attention, both in theoretical research and in practice. From theoretical point of view, an interconnection network can be modelled by a graph, where the vertices of the graph represent the nodes of the network and the edges of the graph represent connections between the nodes in the network. Fault tolerance is an important...