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.

Let G be a connected graph with minimum degree id="M3"> δ and vertex-connectivity id="M4"> κ . The id="M5"> is id="M6"> k -connected if id="M7"> ≥ , maximally id="M8"> = super-connected every vertex-cut isol...

For a given undirected graph G = (V;E; c G ) with edges weighted by nonnegative reals c G : E ! R + , let G (k) stand for the minimum amount of weights which needs to be added to make G k-edge-connected, and G (k) be the resulting graph obtained from G. This paper rst shows that function G over the entire range k 2 [0;+1] can be computed in O(nm+ n 2 logn) time, and then shows that all G (k) in...

One of Frank Boesch’s best known papers is ‘The strongest monotone degree conditions for n-connectedness of a graph’ [1]. In this paper, we give a simple sufficient degree condition for a graph to be k-edge-connected, and also give the strongest monotone condition for a graph to be 2-edge-connected.

Theorem 1 was the starting point for many other suÆ ient onditions for = Æ. Lesniak [9℄ weakened the ondition Æ bn=2 to deg(u) + deg(v) n for all pairs of nonadja ent verti es u and v in G. Plesn k [10℄ showed that every graph of diameter 2 satis es = Æ and thus generalized Lesniak's result. Improvements of Plesn k's result an be found in Plesn k, Zn am [11℄ and Dankelmann, Volkmann [4℄ (see al...

Let a and b be integers 4 ≤ a ≤ b. We give simple, sufficient conditions for graphs to contain an even [a, b]-factor. The conditions are on the order and on the minimum degree, or on the edge-connectivity of the graph.

The traditional parameter used as a measure of vulnerability of a network modeled by a graph with perfect nodes and edges that may fail is the edge connectivity λ. Of course , () p q K p λ = where p q ≤. In that case, failure of the network simply means that the surviving subgraph becomes disconnected upon the failure of individual edges. If, instead, failure of the network is defined to mean t...