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.
📌 3 Maddede Bu Makale
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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı: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.
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.
Barrientos, C. (2022). On the generation of alpha graphs. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 9 Sayı: 2, 31–43. https://doi.org/10.13069/jacodesmath.1111733
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