12,764 research outputs found
On the Signed -independence Number of Graphs
In this paper, we study the signed 2-independence number in graphs and give new sharp upper and lower bounds on the signed 2-independence number of a graph by a simple uniform approach. In this way, we can improve and generalize some known results in this area
A Survey on Alliances and Related Parameters in Graphs
In this paper, we show that several graph parameters are known in different areas under completely different names.More specifically, our observations connect signed domination, monopolies, -domination, -independence,positive influence domination,and a parameter associated to fast information propagationin networks to parameters related to various notions of global -alliances in graphs.We also propose a new framework, called (global) -alliances, not only in order to characterizevarious known variants of alliance and domination parameters, but also to suggest a unifying framework for the study of alliances and domination.Finally, we also give a survey on the mentioned graph parameters, indicating how results transfer due to our observations
Approximate Zero Modes for the Pauli Operator on a Region
Let denoted the Pauli operator on a bounded open
region with Dirichlet boundary conditions and
magnetic potential scaled by some . Assume that the corresponding
magnetic field satisfies where and is an open subset of
of full measure (note that, the Orlicz space
contains for any ). Let
denote the corresponding eigenvalue counting function. We establish the strong
field asymptotic formula as , whenever
for some and . The
corresponding eigenfunctions can be viewed as a localised version of the
Aharonov-Casher zero modes for the Pauli operator on .Comment: 28 pages; for the sake of clarity the main results have been
reformulated and some minor presentational changes have been mad
- …