Rotation matrices for vertex maps on graphs

Abstract

Let G be a finite connected graph. Suppose is a map homotopic to the identity that permutes the vertices. For such a map, a rotation matrix is defined and the basic properties of this matrix are given. It is shown that this matrix generalizes some of the information given by the rotation interval, which is defined when the graph is a circle, to more general graphs.

Keywords:

• graphs
• vertex maps
• periodic orbits
• rotation matrix
• rotation interval

2000 Mathematics Subject Classification::

• 37E15
• 37E25
• 37E45