Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...

Kautz digraphs K(d, `) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz digraphs CK(d, `) were recently introduced by Böhmová, Huemer and the author, and some of its distance-related parameters were fixed. In this paper we propose a new approach to cyclic Kautz digraphs by introducing the family ...

A connected digraph of minimum degree δ is said to be maximally connected if the cardinality of every cutset is al least δ, and it is called superconnected if moreover every minimum disconnecting set F consists of the vertices adjacent to or from a given vertex not belonging to F . Let π be an integer, 0 ≤ π ≤ δ − 2, δ being the minimum degree of the digraph. In this work, we prove that if D ≤ ...

Let G be a connected graph with minimum degree δ and edgeconnectivity λ. A graph is maximally edge-connected if λ = δ, and it is superedge-connected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. In this paper, we show that a connected graph or a connected triangle-free graph is maximally edge-connected or sup...

Let G=( V, E) be a digraph with diameter D # 1. For a given integer 1 t. The t-distance edge-connectivity of G is defined analogously. This paper studies some results on the distance connectivities of digraphs and bipartite digraphs. These ...

For designing reliable and efficient communications networks, the problem of constructing a maximally connected d-regular digraph (directed graph) with a small diameter is investigated. A maximally connected d-regular digraph with a diameter at most two larger than the lower bound for any number of nodes n > 2d and any d > 3 is constructed. Since the diameter of this digraph is quasiminimal (at...

Recently, it was proved that if the diameter D of a graph G is small enough in comparison with its girth, then G is maximally connected and that a similar result also holds for digraphs. More precisely, if the diameter D of a digraph G satisfies D 5 21 1, then G has maximum connectivity ( K = 6 ) . and if D 5 21, then it attains maximum edge-connectivity ( A = 6 ) , where I is a parameter which...

 It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.