The restricted edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks. This paper determines that the restricted edge-connectivity of the de Bruijn digraph B(d, n) is equal to 2d − 2 for d ≥ 2 and n ≥ 2 except B(2, 2). As consequences, the super edge-connectedness of B(d, n) is obtained immediately.

The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability indices than the connectivity and the edge-connectivity. This paper shows that for a connected balanced digraph D and its line digraph L, if D is optimally super edge-connected, then κ1(L) = 2λ1(D), and that for a connected graph G and its line graph L, if one of κ1(L) and λ2(G) exists, then κ1...

Figueroa-Centeno et al. introduced the following product of digraphs: let D be a digraph and let Γ be a family of digraphs such that V (F ) = V for every F ∈ Γ. Consider any function h : E(D) −→ Γ. Then the product D ⊗h Γ is the digraph with vertex set V (D) × V and ((a, x), (b, y)) ∈ E(D ⊗h Γ) if and only if (a, b) ∈ E(D) and (x, y) ∈ E(h(a, b)). In this paper, we deal with the undirected vers...

Recently, some sufficient conditions for a digraph to have maximum connectivity or high superconnectivity have been given in terms of a new parameter which can be thought of as a generalization of the girth of a graph. In this paper similar results are derived for bipartite digraphs and graphs showing that, in this case, all the known conditions can be improved. As a corollary, it is shown that...

It is shown in this work that all n-dimensional hypercube networks for n P 4 are maximally 3-restricted edge connected. Employing this observation, we analyze the reliability of hypercube networks and determine the first 3n 5 coefficients of the reliability polynomial of n-cube networks. 2010 Published by Elsevier Inc.

0. Initiated by Sekanina [6], in the sixties and more intensively in the seventies there were considered powers of undirected graphs with special respect to their Hamiltonian behaviour. These investigations have resulted in a lot of interesting and partly very profound propositions; we only remind of the (simple) result of Sekanina [6] that the cube of every finite connected graph is Hamiltonia...

The vertex connectivity k of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding Ž 3 separator. The time for a digraph having n vertices and m edges is O min k q 4 . n, k n m ; for an undirected graph the term m can be replaced by k n. A ran...

We consider finite and simple digraphs. Usually, we use G to denote a graph and D to a digraph. Undefined terms and notations will follow [6] for graphs and [3] for digraphs. In particular, κ(G), κ′(G), α(G) ans α′(G) denote the connectivity, the edge connectivity, the independence number, and the matching number of a graph G; and λ(D) denotes the arc-strong connectivity of a digraph D as well ...