Graph distance‐dependent labeling related to code assignment in computer networks

For nonnegative integers d₁, d₂, and L(d₁, d₂)‐labeling of a graph G, is a function f : V(G) → {0, 1, 2, …} such that |f(u) − f(v)| ≥ d_i whenever the distance between u and v is i in G, for i = 1, 2. The L(d₁, d₂)‐number of G, λ(G) is the smallest k such that there exists an L(d₁, d₂)‐labeling with the largest label k. These labelings have an application to a computer code assignment problem. The task is to assign integer “control codes” to a network of computer stations with distance restrictions, which allow d₁ ≤ d₂. In this article, we will study the labelings with (d₁, d₂) ∈ {(0, 1), (1, 1), (1, 2)}. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

State and society in Asia

India and China are the 2 most populous countries of the world; in the 1950s, both countries initiated a centrally planned program for rapid development within vastly differing political systems. China embarked India's policy encouraged only voluntary acceptance of family planning. In both cases, however, government involvement in population forms a part of comprehensive national planning. Both countries rely on a limited resource base and technological sophistication in order to alleviate mass poverty and misery. The political implications of population growth cannot be neatly isolated from those that are generated by social and economic forces of change in a society that is in a transitional stage of modernization and development. Development has not been an unmixed bleesing; population growth is one of its counterproductive outcomes. The development process has begun to draw increasing attention to hitherto neglected correlates of fertility decline, such as a reduction in infant mortality, universal education, improvement in women's status, and women's participation in economic activity outside the home, all of which eventually result in greater demand for family planning services. Both the Indian and Chinese models highlight the importance of taking the people into one's confidence; the response of the common people to official initiatives is critical in securing a reduction in fertility levels. China has adopted a 1 child family policy, yet it is unreasonable to expect that the Indian people would agree to a nationally prescribed family size norm below 2 children. The principal determinant of future population trends in both these countries is the course of their politics. The success of developing countries will be assured if the developed nations support their progress without being worried about their population growth, which is the result of their unavoidable failure to modernize their social and economic structures.