Tea at 3:30 pm in SC 1425. (Contact Person: Ralph McKenzie)

]]>To characterize the underlying graphs for which this resilient consensus is always possible, we present the notion of r-robustness in graphs. An undirected graph G(V,E) is r-robust if for every pair of non-empty and disjoint subsets S1 and S2 of V, there is a vertex v in Si having at least r neighbors in V/Si, where i in {1,2} . The property of r-robustness, in general, is a stronger indicator of structural robustness than the traditional metric of graph connectivity. We study the r-robustness in different graphs, and present results regarding the construction of r-robust graphs. Finally, we present how we can improve the r-robustness in graphs by introducing some special vertices called as ‘trusted nodes’.

]]>Contact Person: Gennadi Kasparov

]]>Tea at 3:30 pm in SC 1425. (Contact Person: Denis Osin)

]]>