Let G be a graph on n vertices and m edges. An edge is written xy (equivalently yx). A dominating set in G is a set of vertices D such that every vertex of G is either in D or is adjacent to some vertex of D. It is said to be minimal if it does not contain any other dominating set as a proper subset. For every vertex x let N [x] be {x} ∪ {y | xy ∈ E}, and for every S ⊆ V let N [S] := ⋃ x∈S N [x...

We consider the graphs Hn a defined as the Cartesian products of n complete graphs with a vertices each. Let an edge cut partition the vertex set of a graph into k subsets A1, . . . , Ak with ||Ai| − |Aj || ≤ 1. We consider the problem of determining the minimal size of such a cut for the graphs defined above and present bounds and asymptotic results for some specific values of k.

The Minimum Coloring Cut Problem is defined as follows: given a connected graph G with colored edges, find an edge cut E′ of G (a minimal set of edges whose removal renders the graph disconnected) such that the number of colors used by the edges in E′ is minimum. In this work, we present two approaches based on Variable Neighborhood Search to solve this problem. Our algorithms are able to find ...

MOTIVATION Structural studies of metabolic networks yield deeper insight into topology, functionality and capabilities of the metabolisms of different organisms. Here, we address the analysis of potential failure modes in metabolic networks whose occurrence will render the network structurally incapable of performing certain functions. Such studies will help to identify crucial parts in the net...