2009 Student Research Conference:

22nd Annual Student Research Conference

22nd Annual Student Research Conference

**Properties of K-Saturated Graphs**

Amanda Day

Dr. Michael Adams , Faculty Mentor

We are interested in studying a special class of graphs called k-saturated graphs. The case when k = 1 is trivial. Families of graphs which are k- saturated where k = 2, 3 are known. We are interested in the existence or non-existence of k-saturated graphs when k = 4. We will present some general conditions which must hold for a graph to be k-saturated, including results about the diameter of these graphs, the minimum degree at each vertex, and the existence of large sets of independent vertices in the graph. In addition we will give examples to demonstrate these properties.

**Keywords:** graph theory, diameter, minimum degree, independent set

**Topic(s):**Mathematics

**Presentation Type:** Oral Paper

**Session:** 11-2

**Location:** VH 1328

**Time:** 8:30