Generating functions and regular languages of walks with modular restrictions in graphs

• Main Author: Rahm, Ludwig
• Format: Others
• Language: English
• Published: Linköpings universitet, Matematik och tillämpad matematik 2017
• Subjects: Graph Theory; Combinatorics; Generating Function; Voltage Graph; Reg- ular Languages; Dyck’s Paths; Discrete Mathematics; Diskret matematik
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-138117

This thesis examines the problem of counting and describing walks in graphs, and the problem when such walks have modular restrictions on how many timesit visits each vertex. For the special cases of the path graph, the cycle graph, the grid graph and the cylinder graph, generating functions and regular languages for their walks and walks with modular restrictions are constructed. At the end of the thesis, a theorem is proved that connects the generating function for walks in a graph to the generating function for walks in a covering graph.