A permutation graph G of a graph G (or generalized prism) is obtained by taking two disjoint copies of G and adding an arbitrary matching between the copies. For the parameters diameter, radius, average distance, connectivity and edge-connectivity, we compare the values of the parameter for G and G. In particular we show that if G has no isolates and is not 2Kk for k odd, then there exists a pe...

We give the first O(t log t) time algorithm for processing a given sequence of t edge updates and 3-vertex/edge connectivity queries in an undirected unweighted graph. Our approach builds upon a method by Eppstein [Epp94] that reduces graphs to smaller equivalents on a set of key vertices. It also leads to algorithms for offline 2-vertex/edge connectivity whose performances match those from Kac...

In this paper we present a study about spanning edge betweenness, an edge-based metric for complex network analysis that is defined as the probability of an edge being part of a minimum spanning tree. This probability reflects how redundant an edge is in what concerns the connectivity of a given network and, hence, its value gives information about the network topology. We apply this metric to ...

Restricted edge connectivity is a more refined network reliability index than edge connectivity. A restricted edge cut F of a connected graph G is an edge cut such that G−F has no isolated vertex. The restricted edge connectivity λ′ is theminimumcardinality over all restricted edge cuts.WecallG λ′-optimal if λ′ = ξ , where ξ is theminimum edgedegree inG. Moreover, a λ′-optimal graphG is called ...

Let G = (V, E) be a connected graph. Let G = (V, E) be a connected graph. An edge set F ⊂ E is said to be a k-restricted edge cut, if G− F is disconnected and every component of G− F has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is the cardinality of a minimum k-restricted edge cut of G. A graph G is λk-connected, if G contains a k-restricted edge cut. A λk...