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- Graph theory (3)
- Combinatorial games (2)
- Covering (2)
- Packing (2)
- Peg solitaire (2)
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- 4-cycle (1)
- Angle bisector (1)
- Antibiotic-resistant bacteria (1)
- Bipartite graph (1)
- Cactus graph (1)
- Cartesian product (1)
- Contradiction (1)
- Crossing times (1)
- Crossing times models (1)
- Decomposition (1)
- Decompositon (1)
- Design theory (1)
- Deterministic model (1)
- Experimental design (1)
- Extremal graph theory (1)
- Games on graph (1)
- Games on graphs (1)
- Hexagon (1)
- Isosceles (1)
- Level crossing (1)
- Math finance (1)
- Steiner-Lehmus (1)
- Stochastic model (1)
- Very cost effective partition (1)
- Wald's applications (1)
Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Extremal Results For Peg Solitaire On Graphs, Aaron D. Gray
Extremal Results For Peg Solitaire On Graphs, Aaron D. Gray
Electronic Theses and Dissertations
In a 2011 paper by Beeler and Hoilman, the game of peg solitaire is generalized to arbitrary boards. These boards are treated as graphs in the combinatorial sense. An open problem from that paper is to determine the minimum number of edges necessary for a graph with a fixed number of vertices to be solvable. This thesis provides new bounds on this number. It also provides necessary and sufficient conditions for two families of graphs to be solvable, along with criticality results, and the maximum number of pegs that can be left in each of the two graph families.
Packings And Coverings Of Complete Graphs With A Hole With The 4-Cycle With A Pendant Edge, Yan Xia
Packings And Coverings Of Complete Graphs With A Hole With The 4-Cycle With A Pendant Edge, Yan Xia
Electronic Theses and Dissertations
In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs Kv, (2) complete bipartite graphs Km,n, and (3) complete graphs with a hole K(v,w).
Very Cost Effective Partitions In Graphs, Inna Vasylieva
Very Cost Effective Partitions In Graphs, Inna Vasylieva
Electronic Theses and Dissertations
For a graph G=(V,E) and a set of vertices S, a vertex v in S is said to be very cost effective if it is adjacent to more vertices in V -S than in S.
A bipartition pi={S, V- S} is called very cost effective if both S and V- S are very cost effective sets. Not all graphs have a very cost effective bipartition, for example, the complete graphs of odd order do not. We consider several families of graphs G, including Cartesian products and cacti graphs, to determine whether G has a very cost effective bipartition.
Restricted And Unrestricted Coverings Of Complete Bipartite Graphs With Hexagons, Wesley M. Surber
Restricted And Unrestricted Coverings Of Complete Bipartite Graphs With Hexagons, Wesley M. Surber
Electronic Theses and Dissertations
A minimal covering of a graph G with isomorphic copies of graph H is a set {H1, H2, H3, ... , Hn} where Hi is isomorphic to H, the vertex set of Hi is a subset of G, the edge set of G is a subset of the union of Hi's, and the cardinality of the union of Hi's minus G is minimum. Some studies have been made of covering the complete graph in which case an added condition of the edge set of Hi …
Peg Solitaire On Trees With Diameter Four, Clayton A. Walvoort
Peg Solitaire On Trees With Diameter Four, Clayton A. Walvoort
Electronic Theses and Dissertations
In a paper by Beeler and Hoilman, the traditional game of peg solitaire is generalized to graphs in the combinatorial sense. One of the important open problems in this paper was to classify solvable trees. In this thesis, we will give necessary and sufficient conditions for the solvability for all trees with diameter four. We also give the maximum number of pegs that can be left on such a graph under the restriction that we jump whenever possible.
A Variety Of Proofs Of The Steiner-Lehmus Theorem, Sherri R. Gardner
A Variety Of Proofs Of The Steiner-Lehmus Theorem, Sherri R. Gardner
Electronic Theses and Dissertations
The Steiner-Lehmus Theorem has garnered much attention since its conception in the 1840s. A variety of proofs resulting from the posing of the theorem are still appearing today, well over 100 years later. There are some amazing similarities among these proofs, as different as they seem to be. These characteristics allow for some interesting groupings and observations.
Level Crossing Times In Mathematical Finance, Ofosuhene Osei
Level Crossing Times In Mathematical Finance, Ofosuhene Osei
Electronic Theses and Dissertations
Level crossing times and their applications in finance are of importance, given certain threshold levels that represent the "desirable" or "sell" values of a stock. In this thesis, we make use of Wald's lemmas and various deep results from renewal theory, in the context of finance, in modelling the growth of a portfolio of stocks. Several models are employed .
A Mathematical Model For Antibiotic Resistance In A Hospital Setting With A Varying Population, Edward H. Snyder
A Mathematical Model For Antibiotic Resistance In A Hospital Setting With A Varying Population, Edward H. Snyder
Electronic Theses and Dissertations
Antibiotic-resistant bacteria(ARB) is causing increased health risk and cost to society. Mathematical models have been developed to study the transmission of resistant bacteria and the efficacy of preventive measures to slow its spread within a hospital setting. The majority of these models have assumed a constant total hospital population with the admission and discharge rates being equal throughout the duration. But a typical hospital population varies from day to day and season to season. In this thesis, we apply variable admission and discharge daily rates to existing deterministic and stochastic models which examine the transmission of single and dual resistant …