Sunlet factors for Cartesian products of cycles

TL;DR

This paper explores how sunlets, a cycle with pendant edges, can be used to factorize bipartite toroidal grid graphs through specific homomorphisms, revealing new structural insights.

Contribution

It introduces a novel approach to factorize bipartite toroidal grids into sunlets via homomorphisms from disjoint unions of sunlets, expanding understanding of graph decompositions.

Findings

Factorizations into sunlets are characterized for bipartite toroidal grids.

Homomorphisms from unions of sunlets provide bijective edge mappings.

Results apply to grids with dimensions $2n$ by $2n$, $n geq 3$.

Abstract

A sunlet is a cycle with a pendant edge attached at each vertex of the cycle. For the bipartite toroidal grid graphs $C_{2n} \Box C_{2n}$, factorizations into sunlets are given by homomorphisms from disjoint unions of $s$ copies of a sunlet for $s \in \{1, n, n^2\}, n \geq 3$ such that edges are mapped bijectively.