# Some families of $\alpha$-labeled subgraphs of the integral grid

Document Type : Original paper

Authors

1 Department of Mathematics Valencia College Orlando, FL 32832 United States

2 Department of Mathematics Full Sail University Orlando, FL 32792 United States

Abstract

In this work we study the most restrictive variety of graceful labelings, that is, we study the existence of an $\alpha$-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.

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