The Graceful Coalescence of Alpha Cycles

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Communications in Advanced Mathematical Sciences
Volume:2 Issue:2
The Graceful Coalescence of Alpha Cycles

The Graceful Coalescence of Alpha Cycles

Authors : Christian BARRİENTOS, Sarah MİNİON

Pages : 114-120

Doi:10.33434/cams.505485

View : 97 | Download : 8

Publication Date : 2019-06-27

Article Type : Research Paper

Abstract :The standard coalescence of two graphs is extended, allowing to identify two isomorphic subgraphs instead of a single vertex. It is proven here that any succesive coalescence of cycles of size $n$, where $n$ is divisible by four, results in an $\alpha$-graph, that is, the most restrictive kind of graceful graph, when the subgraphs identified are paths of sizes not exceeding $\frac{n}{2}$. Using the coalescence and another similar technique, it is proven that some subdivisions of the ladder $L_n = P_2 \times P_n$ also admit an $\alpha$-labeling, extending and generalizing the existing results for this type of subdivided graphs.
Keywords : Coalescence, alpha labeling, Graceful labeling, Ladder

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