Equal opportunity networks, distance-balanced graphs, and Wiener game

Given a graph G and a set X ⊆ V(G), the relative Wiener index of X in G is defined as WX (G) = {u,v}∈X 2  dG(u, v) . The graphs G (of even order) in which for every partition V(G) = V1 +V2 of the vertex set V(G) such that |V1| = |V2| we haveWV1 (G) = WV2 (G) are called equal opportunity graphs. In this note we prove that a graph G of even order is an equal opportunity graph if and only if it is a distance-balanced graph. The latter graphs are known by several characteristic properties, for instance, they are precisely the graphs G in which all vertices u ∈ V(G) have the same total distance DG(u) = v∈V(G) dG(u, v). Some related problems are posed along the way, and the so-called Wiener game is introduced.

Health, Education and Employment in a Forward-Backward Dichotomy Based on Standard of Living Index for the Tribes in Kerala

The Paper unfolds the paradox that exists in the tribal community with respect to the development indicators and hence tries to cull out the difference in the standard of living of the tribes in a dichotomous framework, forward and backward. Four variables have been considered for ascertaining the standard of living and socio-economic conditions of the tribes. The data for the study is obtained from a primary survey in the three tribal predominant districts of Wayanad, Idukki and Palakkad. Wayanad was selected for studying six tribal communities (Paniya, Adiya, Kuruma, Kurichya, Urali and Kattunaika), Idukki for two communities (Malayarayan and Muthuvan) and Palakkad for one community (Irula). 500 samples from 9 prominent tribal communities of Kerala have been collected according to multistage proportionate random sample framework. The analysis highlights the disproportionate nature of socio-economic indicators within the tribes in Kerala owing to the failure of governmental schemes and assistances meant for their empowerment. The socio-economic variables, such as education, health, and livelihood have been augmented with SLI based on correlation analysis gives interesting inference for policy options as high educated tribal communities are positively correlated with high SLI and livelihood. Further, each of the SLI variable is decomposed using Correlation and Correspondence analysis for understanding the relative standing of the nine tribal sub communities in the three dimensional framework of high, medium and low SLI levels. Tribes with good education and employment (Malayarayan, Kuruma and Kurichya) have a better living standard and hence they can generally be termed as forward tribes whereas those with a low or poor education, employment and living standard indicators (Paniya, Adiya, Urali, Kattunaika, Muthuvans and Irula) are categorized as backward tribes