1,746 research outputs found
Symmetry properties of subdivision graphs
The subdivision graph of a graph is obtained from
by `adding a vertex' in the middle of every edge of \Si. Various
symmetry properties of are studied. We prove that, for a connected
graph , is locally -arc transitive if and only if
is -arc transitive. The diameter of
is , where has diameter and , and local -distance transitivity of is
defined for . In the general case where
we prove that is locally -distance transitive
if and only if is -arc transitive. For the
remaining values of , namely , we classify
the graphs for which is locally -distance transitive in
the cases, and . The cases remain open
A semidefinite programming hierarchy for packing problems in discrete geometry
Packing problems in discrete geometry can be modeled as finding independent
sets in infinite graphs where one is interested in independent sets which are
as large as possible. For finite graphs one popular way to compute upper bounds
for the maximal size of an independent set is to use Lasserre's semidefinite
programming hierarchy. We generalize this approach to infinite graphs. For this
we introduce topological packing graphs as an abstraction for infinite graphs
coming from packing problems in discrete geometry. We show that our hierarchy
converges to the independence number.Comment: (v2) 25 pages, revision based on suggestions by referee, accepted in
Mathematical Programming Series B special issue on polynomial optimizatio
The Gewirtz graph: An exercise in the theory of graph spectra
Graphs;mathematics
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