Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively new field of study. We present a survey of known results concerning vdec colorings. We also define a new matrix which may be used to study vdec colorings, and examine its properties. We find several bounds on the eigenvalues of this matrix, as well as results concerning its determinant, and other properties. We finish by examining related topics and open problems.

There are few published direct measurements of the atmosphere-surface exchange of volatile organic compounds (VOCs), particularly for biogenic VOCs (BVOCs). Global modelling of atmospheric chemistry and transport of BVOCs has large uncertainties due to the very small number of measurements in tropical regions, which are responsible for half the global BVOC emissions. This thesis presents direct measurements of concentrations and ecosystem fluxes of BVOCs in different regions (Tropics, Mediterranean) using the approach of virtual disjunct eddy covariance (vDEC) combined with proton transfer reaction mass spectrometry (PTR-MS) – a real-time BVOC sensor. The field measurements also included methodological developments of the vDEC/PTR-MS approach, which will be of value to the wider flux measurement community. A novel approach to determining the lag time between the vertical wind measurement and the air concentration measurement has been developed that will greatly reduce the uncertainty in the derived flux measurements. In the laboratory, the selectivity of PTR-MS was investigated by designing an alternating drift-voltage mode (AD-PTR-MS) to discriminate between structural isomers detected at the same m/z channel, with monoterpenes used as model compounds. The results of the measurements, particularly from the rainforest and oil palm plantations in Borneo, are novel and therefore provide important experimental constraints on models of atmospheric emissions, chemistry and transport. For example, although parameters which work reasonably well can be derived for model algorithms for the emission of isoprene from the rainforest, their performance over oil palms was less good, because of circadian controls of emissions from oil palms. However, the larger problem is the measured basal emission rates (BERs) which are significantly smaller than those used by default in the global MEGAN model. Another novel finding was the high deposition velocities of MVK and MACR (isoprene first order oxidation products) which at the oil palm plantation commonly exceeded 1 cm s-1; this result has implications for atmospheric modelling. The successful field results relied on significant developments in software for data acquisition and processing, and operational optimisation of the PTR-MS instruments in the extreme humidity encountered during the fieldwork in Borneo.

Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively new field of study. We present a survey of known results concerning vdec colorings. We also define a new matrix which may be used to study vdec colorings, and examine its properties. We find several bounds on the eigenvalues of this matrix, as well as results concerning its determinant, and other properties. We finish by examining related topics and open problems.