Open Access Research

Vertex maps on graphs-trace theorems

Chris Bernhardt

Author Affiliations

Fairfield University, Fairfield, CT 06824, USA

Fixed Point Theory and Applications 2011, 2011:8  doi:10.1186/1687-1812-2011-8

Published: 23 June 2011


The paper proves two theorems concerning the traces of Oriented Markov Matrices of vertex maps on graphs. These are then used to give a Sharkoksky-type result for maps that are homotopic to the identity and that flip at least one edge.

2000 Mathematics Subject Classification

37E15, 37E25

Graphs; Vertex maps; Periodic orbits; Sharkovsky's theorem; Trace