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}
}