Planarity of generalized ladder graphs
Abstract
The Cartesian product of P2 and Pn is called an n-ladder graph for a positive integer n. We call two paths Pm and Pn together with some edges each of which joins a vertex on Pm and a vertex on Pn 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(Pn ,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(Pn ,f).
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