On the relationship between NLC-width and linear NLC-width

AbstractIn this paper, we consider NLC-width, NLCT-width, and linear NLC-width bounded graphs. We show that the set of all complete binary trees has unbounded linear NLC-width and that the set of all co-graphs has unbounded NLCT-width. Since trees have NLCT-width 3 and co-graphs have NLC-width 1, it follows that the family of linear NLC-width bounded graph classes is a proper subfamily of the family of NLCT-width bounded graph classes and that the family of NLCT-width bounded graph classes is a proper subfamily of the family of NLC-width bounded graph classes

A connectivity rating for vertices in networks

We compute the influence of a vertex on the connectivity structure of a directed network by using Shapley value theory. In general, the computation of such ratings is highly inefficient. We show how the computation can be managed for many practically interesting instances by a decomposition of large networks into smaller parts. For undirected networks, we introduce an algorithm that computes all vertex ratings in linear time, if the graph is cycle composed or chordal.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI