Obnoxious Centers in Graphs

The obnoxious center problem on weighted cactus graphs (Extended Abstract)

On Obnoxious Markets

Certain markets evoke popular discomfort, distrust and even outrage. Trade in arms, drugs, toxic waste, child labor and body parts, for example, elicits these reactions to different degrees. This paper asks—what is it about some markets that brings about these responses? It is argued that three key parameters—extremity, agency and inequality—have a bearing on our intuitive reactions and serve t...

Placing an Obnoxious Facility in Geometric Networks

In this paper we consider several different problems of placing an obnoxious facility on geometric networks. In particular, our main results show how to obtain efficient polynomial time algorithms for locating an obnoxious facility on the given network under various distance functions such as maximizing the total sum of distances or maximizing the smallest of the distances from the facility to ...

Smallest graphs with distinct singleton centers

An incredible number of centrality indices has been proposed to date (Todeschini & Consonni, 2009). Four of them, however, can be considered prototypical because they operationalize distinct concepts of centrality and together cover the bulk of analyses and empirical uses: degree, closeness, betweenness, and eigenvector centrality. In teaching any mathematical science, it is instructive to cons...

Centers and medians of distance-hereditary graphs

A graph is distance-hereditary if the distance between any two vertices in a connected induced subgraph is the same as in the original graph. In this paper, we study metric properties of distance-hereditary graphs. In particular, we determine the structures of centers and medians of distance-hereditary and related graphs. The relations between eccentricity, radius, and diameter of such graphs a...