A Variation of

A set S ⊆ V is a dominating set of a graph G = (V, E) if each vertex in V is either in S or is adjacent to a vertex in S. A vertex is said to dominate itself and all its neighbors. The domination number γ (G) is the minimum cardinality of a dominating set of G. A set S ⊆ V is a total dominating set of a graph G = (V,E) if each vertex in V is adjacent to a vertex in S. The total domination number γt (G) is the minimum cardinality of a totally dominating set of G. An immediate bound on γt (G) for graphs with no isolated vertices is γ (G) ≤ γt (G) ≤ 2γ (G) . Thus, for some rational k ∈ [1, 2], γt (G) = k ∗ γ (G) or k = γt(G) γ(G) . Examples of G that realize each boundary value are numerous. We show that every rational k ∈ [1, 2] can be realized by some graph G. Total domination is just one of many flavors of domination. This poster will also present similar results for other domination parameters. Poster #10 Graph Theory: The Alabama State University Postman Problem, Michael Wright, Alabama State University Abstract: Graph theory is a branch of mathematics that is devoted entirely to graphical structures and their composition. Graph theory has many applications in science and industry and can be used to find a solution to any path-related problem. These applications are extended to several problems one being the Traveling Salesman problem. The Travelling Salesman problem is a Hamiltonian cycle. The purpose of this project is to find a Hamiltonian cycle for the Alabama State University Post Office thus simulating The Travelling Salesman problem. Poster #11 Inverse Eigenvalue Problems Arising in Population Models, Tao-hsiang Chang, The Citadel Abstract: In this project, we study the relation of a stable life-cycle model and eigenvalues of the matrix A the model is associated with. We have derived the conditions for elements of A for some stable life cycle models. Some of our proofs are based on MatLab simulation. Life cycle models of frogs with n stages (for n 3) are used to illustrate our results. Poster #12 Solving system of polynomial equations, Anisah NuMan, Spelman College Abstract: Let k be a field and k[x1, . . . , xn] be the polynomial ring in n-variables x1, . . . , xn with coefficients in k. We will use Gr’bner bases technique to solve a system of polynomial equations in k[x1, . . . , xn]. This is a generalization of solving a system of linear equations in Linear algebra.