A SURVEY OF DISTANCE MAGIC GRAPHS

In this report, we survey results on distance magic graphs and some closely related graphs. A distance magic labeling of a graph G with magic constant k is a bijection l from the vertex set to {1, 2, . . . , n}, such that for every vertex x Σ l(y) = k,y∈NG(x) where NG(x) is the set of vertices of G adjacent to x. If the graph G has a distance magic labeling we say that G is a distance magic graph. In Chapter 1, we explore the background of distance magic graphs by introducing examples of magic squares, magic graphs, and distance magic graphs. In Chapter 2, we begin by examining some basic results on distance magic graphs. We next look at results on different graph structures including regular graphs, multipartite graphs, graph products, join graphs, and splitting graphs. We conclude with other perspectives on distance magic graphs including embedding theorems, the matrix representation of distance magic graphs, lifted magic rectangles, and distance magic constants. In Chapter 3, we study graph labelings that retain the same labels as distance magic labelings, but alter the definition in some other way. These labelings include balanced distance magic labelings, closed distance magic labelings, D-distance magic labelings, and distance antimagic labelings. In Chapter 4, we examine results on neighborhood magic labelings, group distance magic labelings, and group distance antimagic labelings. These graph labelings change the label set, but are otherwise similar to distance magic graphs. In Chapter 5, we examine some applications of distance magic and distance antimagic labeling to the fair scheduling of tournaments. In Chapter 6, we conclude with some open problems.

From Mill Gates to Magic City: U.S. Steel and Welfare Capitalism in Gary, Indiana, 1906-1930

Gary, Indiana is a city with indelible ties to industrial paternalism. Founded in 1906 by United States Steel Corporation to house workers of the trust’s showpiece mill, the emergence of this model company town was both the culmination of lessons learned from its predecessors’ mistakes and innovative corporate planning. U.S. Steel’s Progressive Era adaptation of welfare capitalism characterized the young city through a combination of direct community involvement and laissez-faire social control. This thesis examines the reactionary implementation of paternalist policies in Gary between 1906 and 1930 through the purviews of three elements under corporate influence: housing, education, and social welfare. Each category demonstrates how both the corporation and citizenry affected and adapted Gary’s physical and cultural landscape, public perceptions, and community identity. Parallel to the popular narrative throughout is that of Gary’s African-American community, and the controversial circumstances of this population’s segregated development.