Fixed block configuration GDDs with block size 6 and (3, r)-regular graphs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis. In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; λ1; λ2). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s points from one of the two groups and t points from the other. Chapter 2 begins with an overview of previous results and constructions for small group size and block sizes 3, 4 and 5. Chapter 2 is largely devoted to presenting constructions and results about GDDs with two groups and block size 6. We show the necessary conditions are sufficient for the existence of GDD(n, 2, 6; λ1, λ2) with fixed block configuration (3; 3). For configuration (1; 5), we give minimal or nearminimal index constructions for all group sizes n ≥ 5 except n = 10, 15, 160, or 190. For configuration (2, 4), we provide constructions for several families ofGDD(n, 2, 6; λ1, λ2)s. Chapter 3 addresses characterizing (3, r)-regular graphs. We begin with providing previous results on the well studied class of (2, r)-regular graphs and some results on the structure of large (t; r)-regular graphs. In Chapter 3, we completely characterize all (3, 1)-regular and (3, 2)-regular graphs, as well has sharpen existing bounds on the order of large (3, r)- regular graphs of a certain form for r ≥ 3. Finally, the appendix gives computational data resulting from Sage and C programs used to generate (3, 3)-regular graphs on less than 10 vertices.

IMPROVEMENTS IN SUSTAINABILITY OF GRAVITY-FED WATER SYSTEMS IN THE COMARCA NGÄBE-BUGLÉ, PANAMA: SPRING CAPTURES AND CIRCUIT RIDER MODEL

Gravity-flow aqueducts are used to bring clean water from mountain springs in the Comarca Ngäbe-Buglé, Panama, to the homes of the indigenous people who reside there. Spring captures enclose a spring to direct the flow of water into the transmission line. Seepage contact springs are most common, with water appearing above either hard basalt bedrock or a dense clay layer. Spring flows vary dramatically during wet and dry seasons, and discharge points of springs can shift, sometimes enough to impact the capture structure and its ability to properly collect all of the available water. Traditionally, spring captures are concrete boxes. The spring boxes observed by the author were dilapidated or out of alignment with the spring itself, only capturing part of the discharge. An improved design approach was developed that mimics the terrain surrounding the spring source to address these issues. Over the course of a year, three different spring sites were evaluated, and spring captures were designed and constructed based on the new approach. Spring flow data from each case study demonstrate increased flow capture in the improved structures. Rural water systems, including spring captures, can be sustainably maintained by the Circuit Rider model, a technical support system in which technical assistance is provided for the operation of the water systems. During 2012-2013, the author worked as a Circuit Rider and facilitated a water system improvement project while exploring methods of community empowerment to increase the capacity for system maintenance. Based on these experiences, recommendations are provided to expand the Circuit Rider model in the Comarca Ngäbe-Buglé under the Panamanian Ministry of Health’s Water and Sanitation Project (PASAP)