Formulas for the Number of Weak Homomorphisms from Paths to Ladder Graphs and Stacked Prism Graphs - Hatairat Yingtaweesittikul; Sayan Panma; Penying Rochanakul (Journal of Mathematics)
Let G and H be graphs. A mapping f from VG to VH is called a weak homomorphism from G to H if fx=fy or fx,fy∈EH whenever x,y∈EG. A ladder graph is the Cartesian product of two paths, where one of the paths has only one edge. A stacked prism graph is the Cartesian product of a path and a cycle. In this paper, we provide a formula to determine the number of weak homomorphisms from paths to ladder graphs and a formula to determine the number of weak homomorphisms from paths to stacked prism graphs.