#### Document Type

Article

#### Publication Date

7-31-2009

#### First Advisor

Joshua Holden

#### Abstract

We define G(n, k) to be a directed graph whose set of vertices is {0, 1, ..., n−1} and whose set of edges is defined by a modular relation. We say that G(n, k) is symmetric of order m if we can partition G(n, k) into subgraphs, each containing m components, such that all the components in a subgraph are isomorphic. We develop necessary and sufficient conditions for G(n, k) to contain symmetry when n is odd and square-free. Additionally, we use group theory to describe the structural properties of the subgraph of G(n, k) containing only those vertices relatively prime to n.

#### Recommended Citation

Kramer-Miller, Joseph, "Structural Properties of Power Digraphs Modulo n" (2009). *Mathematical Sciences Technical Reports (MSTR)*. 11.

http://scholar.rose-hulman.edu/math_mstr/11

## Comments

MSTR 09-06