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Graceful Labellings of Various Cyclic Snakes

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arxiv 2012.10341 v2 pith:OTSEMORS submitted 2020-12-18 math.CO

Ahmad H. Alkasasbeh , Danny Dyer This is my paper · ORCID
classification math.CO
keywords cyclicgracefulsnakesconditioncycleseverylabellinglengths
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abstract

In this paper, we present a new sufficiency condition to obtain a graceful labelling for every $kC_{4n}$ snake and use this condition to label every such snake for $n=1,2,\ldots,6$. Then, we extend this result to cyclic snakes where the cycles lengths vary. Also, we obtain new results on the (near) graceful labelling of cyclic snakes based on cycles of lengths $n=6, 10, 14$, completely solving the case $n=6$.

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  1. Gracefulness of two nested cycles: a first approach

    math.CO 2024-11 conditional novelty 6.0 of 10

    Every snowflake graph is conservative exactly when its edge count is 0 or 3 modulo 4, and large two-nested-cycle graphs admit matching graceful or near-graceful labelings.

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