@article{article_1111733, title={On the generation of alpha graphs}, journal={Journal of Algebra Combinatorics Discrete Structures and Applications}, volume={9}, pages={31–43}, year={2022}, DOI={10.13069/jacodesmath.1111733}, author={Barrientos, Christian}, keywords={$\alpha$}-labeling, Graceful graph, Amalgamation, Duplication, Replication}, abstract={Graceful labelings constitute one of the classical subjects in the area of graph labelings; among them, the most restrictive type are those called {$\alpha$}-labelings. In this work, we explore new techniques to generate {$\alpha$}-labeled graphs, such as vertex and edge duplications, replications of the entire graph, and $k$-vertex amalgamations. We prove that for some families of graphs, it is possible to duplicate several vertices or edges. Using $k$-vertex amalgamations we obtain an {$\alpha$}-labeling of a graph that can be decomposed into multiple copies of a given {$\alpha$}-labeled graph as well as a robust family of irregular grids that can {$\alpha$}-labeled.}, number={2}, publisher={iPeak Academy}