@article { author = {Barrientos, Christian and Minion, Sarah}, title = {Some families of $\alpha$-labeled subgraphs of the integral grid}, journal = {Communications in Combinatorics and Optimization}, volume = {8}, number = {1}, pages = {77-101}, year = {2023}, publisher = {Azarbaijan Shahid Madani University}, issn = {2538-2128}, eissn = {2538-2136}, doi = {10.22049/cco.2021.26989.1175}, 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.}, keywords = {graceful,α-labeling,harmonious,polyomino,fence}, url = {http://comb-opt.azaruniv.ac.ir/article_14305.html}, eprint = {http://comb-opt.azaruniv.ac.ir/article_14305_0bd702cdba73b058600a24b871f835ca.pdf} }