Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

Characteristics of Upper Troposphere and Lower Stratosphere in Relation to Asian Summer Monsoon

The present work is an attempt to understand the characteristics of the upper troposphere and lower stratosphere over the Asian summer monsoon region, more specifically over the Indian subcontinent. Mainly three important parameters are taken such as zonal wind, temperature and ozone over the UT/LS of the Asian summer monsoon region. It made a detailed study of its interannual variability and characteristics of theses parameters during the Indian summer monsoon period. Monthly values of zonal wind and temperature from the NCEP/NCAR reanalysis for the period 1960-2002 are used for the present study. Also the daily overpass total ozone data for the 12 Indian stations (from low latitude to high latitudes) from the TOMS Nimbus 7 satellite for the period 1979 to 1992 were also used to understand the total ozone variation over the Indian region. The study reveals that if QBO phases in the stratosphere is easterly or weak westerly then the respective monsoon is found to be DRY or below Normal . On the other hand, if the phase is westerly or weak easterly the respective Indian summer monsoon is noted as a WET year. This connection of stratospheric QBO phases and Indian summer monsoon gives more insight in to the long-term predictions of Indian summer monsoon rainfall. Wavelet analysis and EOF methods are the two advanced statistical techniques used in the present study to explore more information of the zonal wind that from the smaller scale to higher scale variability over the Asian summer monsoon region. The interannual variability of temperature for different stratospheric and tropospheric levels over the Asian summer monsoon region have been studied. An attempt has been made to understand the total ozone characteristics and its interannual variablilty over 12 Indian stations spread from south latitudes to north latitudes. Finally it found that the upper troposphere and lower stratosphere contribute significantly to monsoon variability and climate changes. It is also observed that there exists a link between the stratospheric QBO and Indian summer monsoon