The domination polynomial D(G,x) of a graph G is the generating function of its dominating sets. We prove that D(G,x) satisfies a wide range of reduction formulas. We show linear recurrence relations for D(G,x) for arbitrary graphs and for various sp
ecial cases. We give splitting formulas for D(G,x) based on articulation vertices, and more generally, on splitting sets of vertices.
Three Gas-Electron-Multiplier tracking detectors with an active area of 10 cm x 10 cm and a two-dimensional, laser-etched orthogonal strip readout have been tested extensively in particle beams at the Meson Test Beam Facility at Fermilab. These detec
tors used GEM foils produced by Tech-Etch, Inc. They showed an efficiency in excess of 95% and spatial resolution better than 70 um. The influence of the angle of incidence of particles on efficiency and spatial resolution was studied in detail.
Future measurements of the flavor-separated spin structure of the proton via parity-violating W boson production at RHIC require an upgrade of the forward tracking system of the STAR detector. This upgrade will allow the reconstruction of the charge
sign of electrons and positrons produced from decaying W bosons. A design based on six large area triple GEM disks using GEM foils produced by Tech-Etch Inc. has emerged as a cost-effective solution to provide the necessary tracking precision. We report first results from a beam test of three test detectors using Tech-Etch produced GEM foils and a laser etched two dimensional strip readout. The detectors show good operational stability, high efficiency and a spacial resolution of around 70 um or better, exceeding the requirements for the forward tracking upgrade. The influence of the angle of incidence of the particles on the spatial resolution of the detectors has also been studied in detail.
