2005 Ohio Student Research Forum

Abstract

Symmetry and Cyclic Accessibility in Finite Graphs
Syvillia Averett
Ohio State University, Department of Mathematics
Mentor: Dr. Henry Glover

We study the observed fact that most connected symmetric finite graphs are cyclic accessible or in other words have a Hamilton cycle, a cycle in the graph passing through every vertex exactly once. In particular, there exist only four known connected symmetric finite graphs in which there does not exist a Hamilton cycle. In this study we construct Hamilton cycles in symmetric graphs that are tessellations of surfaces to support the conjecture that, except for the four currently known counterexamples, every connected symmetric finite graph has a Hamilton cycle.