Non-contractible non-edges in 2-connected graphs

Any pair of non-adjacent vertices forms a non-edge in a graph. Contraction of a non-edge merges two non-adjacent vertices into a single vertex such that the edges incident on the non-adjacent vertices are now incident on the merged vertex. In this paper, we consider simple connected graphs, hence parallel edges are removed after contraction. The minimum number of nodes whose removal disconnects the graph is the connectivity of the graph. We say a graph is k-connected, if its connectivity is k. A non-edge in a k-connected graph is contractible if its contraction does not result in a graph of lower connectivity. Otherwise the non-edge is non-contractible. We focus our study on non-contractible non-edges in 2-connected graphs. We show that cycles are the only 2-connected graphs in which every non-edge is non-contractible. (C) 2010 Elsevier B.V. All rights reserved.

Thunderstorm climatology and lightning location applications in northern Europe

Thunderstorm is a dangerous electrical phenomena in the atmosphere. Thundercloud is formed when thermal energy is transported rapidly upwards in convective updraughts. Electrification occurs in the collisions of cloud particles in the strong updraught. When the amount of charge in the cloud is large enough, electrical breakdown, better known as a flash, occurs. Lightning location is nowadays an essential tool for the detection of severe weather. Located flashes indicate in real time the movement of hazardous areas and the intensity of lightning activity. Also, an estimate for the flash peak current can be determined. The observations can be used in damage surveys. The most simple way to represent lightning data is to plot the locations on a map, but the data can be processed in more complex end-products and exploited in data fusion. Lightning data serves as an important tool also in the research of lightning-related phenomena, such as Transient Luminous Events. Most of the global thunderstorms occur in areas with plenty of heat, moisture and tropospheric instability, for example in the tropical land areas. In higher latitudes like in Finland, the thunderstorm season is practically restricted to the summer season. Particular feature of the high-latitude climatology is the large annual variation, which regards also thunderstorms. Knowing the performance of any measuring device is important because it affects the accuracy of the end-products. In lightning location systems, the detection efficiency means the ratio between located and actually occurred flashes. Because in practice it is impossible to know the true number of actually occurred flashes, the detection efficiency has to be esimated with theoretical methods.