English

Planarity of generalized ladder graphs

Combinatorics 2022-08-30 v1

Abstract

The Cartesian product of P_2 and P_n is called an n-ladder graph for a positive integer n. We call two paths P_m and P_n together with some edges each of which joins a vertex on P_m and a vertex on P_n a generalized (m,n)-ladder graph. In this paper, we completely characterize the planar generalized ladder graphs and the outerplanar generalized ladder graphs. A functigraph C(P_n ,f) is a generalized (n,n)-ladder graph. Consequently, our result solves the problem posed by A. Chen et al. (2011) to characterize planar functigraphs C(P_n ,f).

Keywords

Cite

@article{arxiv.2208.13637,
  title  = {Planarity of generalized ladder graphs},
  author = {Hojin Chu and Suh-Ryung Kim and Homoon Ryu},
  journal= {arXiv preprint arXiv:2208.13637},
  year   = {2022}
}