2 citations · 4 across the 10 of their papers we have counts for
4 papers · 1 filter
Recurrence relations and splitting formulas for the domination polynomial
Tomer Kotek, James Preen, Frank Simon +2
The domination polynomial D(G,x) of a graph G is the generating function of its dominating sets. We prove that D(G,x) satisfies a wide range of reduction formulas. We show linear r…
Splitting the K-Terminal Reliability
Frank Simon
Let G=(V,E) be a graph and K a set of terminal vertices of G. Assume that the edges of G are failing independently with given probabilities. The K-terminal reliability R(G,K) is th…
Random Information Spread in Networks
Raymond Lapus, Frank Simon, Peter Tittmann
Let G=(V,E) be an undirected loopless graph with possible parallel edges and s and t be two vertices of G. Assume that vertex s is labelled at the initial time step and that every…
Counting Connected Set Partitions of Graphs
Frank Simon, Peter Tittmann, Martin Trinks
Let be a simple undirected graph with vertices then a set partition of the vertex set of is a connected set partition if each subgraph $G[V_…