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DM
2008
58views more  DM 2008»
13 years 7 months ago
The vertex isoperimetric problem for the powers of the diamond graph
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...
Sergei L. Bezrukov, Miquel Rius, Oriol Serra
CORR
2006
Springer
128views Education» more  CORR 2006»
13 years 7 months ago
The Shannon capacity of a graph and the independence numbers of its powers
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...
Noga Alon, Eyal Lubetzky
SODA
2001
ACM
138views Algorithms» more  SODA 2001»
13 years 8 months ago
The diameter of random massive graphs
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...
Linyuan Lu
IPSN
2005
Springer
14 years 29 days ago
Coverage and hole-detection in sensor networks via homology
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...
Robert Ghrist, Abubakr Muhammad
GC
2010
Springer
13 years 6 months ago
Polyhedral Suspensions of Arbitrary Genus
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...
Serge Lawrencenko