Given a connected graph G and a failure probability pe for each edge e in G, the reliability of G is the probability that G remains connected when each edge e is removed independe...
We study a problem on edge percolation on product graphs G× K2. Here G is any finite graph and K2 consists of two vertices {0, 1} connected by an edge. Every edge in G × K2 is p...
The k-Leaf Power recognition problem is a particular case of graph power problems: For a given graph it asks whether there exists an unrooted tree--the k-leaf root--with leaves on...
We introduce some equivalence relations on graphs and posets and prove that they are closed under the cartesian product operation. These relations concern the edge-isoperimetric p...
In the Survivable Network Design Problem (SNDP) the goal is to find a minimum cost subset of edges that satisfies a given set of pairwise connectivity requirements among the ver...