Some families of α-labeled subgraphs of the integral grid

In this work we study the most restrictive variety of graceful labelings, that is, we study the existence of an α-labeling for some families of graphs that can be embedded in the integral grid. Among the categories of graphs considered here we have a subfamily of 2-link fences, a subfamily of column-convex polyominoes, and a subfamily of irregular cyclic-snakes. We prove that under some conditions, the a-labelings of these graphs can be transformed into harmonious labelings. We also present a closed formula for the number of 2-link fences examined here.