We introduce a new graph for all whose cartesian powers the vertex isoperimetric problem has nested solutions. This is the fourth kind of graphs with this property besides the wel...
The independence numbers of powers of graphs have been long studied, under several definitions of graph products, and in particular, under the strong graph product. We show that t...
Many massive graphs (such as the WWW graph and Call graphs) share certain universal characteristics which can be described by so-called the "power law". Here we determin...
We consider coverage problems in sensor networks of stationary nodes with minimal geometric data. In particular, there are no coordinates and no localization of nodes. We introduc...
A new class of polyhedra is discovered—bipyramids of arbitrarily prescribed genus. A two-dimensional generalization of Fáry’s Theorem is established. A purely combinatorial de...