On the generation of alpha graphs

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.

Received: 3 February 2021 | Accepted: 22 October 2021