On the number of congruence classes of paths

Zhicong Lin; Jiang Zeng

On the number of congruence classes of paths

Combinatorics 2011-12-20 v1

Authors: Zhicong Lin , Jiang Zeng

Abstract

Let $P_n$ denote the undirected path of length $n-1$ . The cardinality of the set of congruence classes induced by the graph homomorphisms from $P_n$ onto $P_k$ is determined. This settles an open problem of Michels and Knauer (Disc. Math., 309\ (2009)\ 5352-5359). Our result is based on a new proven formula of the number of homomorphisms between paths.

Keywords

graph homomorphism congruence class path graph enumeration open problem

Cite

@article{arxiv.1112.4026,
  title  = {On the number of congruence classes of paths},
  author = {Zhicong Lin and Jiang Zeng},
  journal= {arXiv preprint arXiv:1112.4026},
  year   = {2011}
}

Comments

11 pages, 2 figures, to appear in Discrete Mathematics

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