#### Date of Defense

Fall 11-28-1990

#### Department

Mathematics

#### First Advisor

Gary Chartrand, Mathematics and Statistics

#### Second Advisor

Arthur White, Mathematics and Statistics

#### Third Advisor

S.F. Kapoor, Mathematics and Statistics

#### Abstract

The induced rotation number ih(G) of a graph G is the minimum order of a graph F such that for every vertex x of G and every vertex y of F, there exists an embedding of G as an induced subgraph of F with x at y. It is shown that ih(G) is defined for every graph G and that the induced rotation number of a graph and its complement are equal. The induced rotation ratio ir(G) of a graph G is defined as the ratio ih(G)/|V(G)|. We show that for every rational number r ∈ [1,2), there exists a graph G for which ir(G)=r. The induced rotation number is extended to two or more graphs and discussed.

#### Recommended Citation

Gavlas, Heather Jordan, "Induced Rotation Numbers of Graphs" (1990). *Honors Theses*. 266.

http://scholarworks.wmich.edu/honors_theses/266

#### Access Setting

Honors Thesis-Campus Only