On the generation of alpha graphs

Year 2022, Volume: 9 Issue: 2, 31 - 43, 13.05.2022

Christian Barrientos

https://doi.org/10.13069/jacodesmath.1111733

Cited By: 1

https://izlik.org/JA56SX27KM

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.

Keywords

{$\alpha$}-labeling , Graceful graph , Amalgamation , Duplication , Replication

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