Edge-odd Graceful Labelings for Dumbbell Graph and Paddle Graph
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Abstract
This article construct edge-odd labelings for dumbbell graph and paddle graph, respectively. The dumbbell graph is constructed by connecting two cycle graphs by an edge, for
and the paddle graph is constructed by connecting two fan graphs
by an edge, for
. We then proof that the constructed labelings are an edge-odd graceful labeling of the dumbbell graph for
and an edge-odd graceful labeling of the paddle graph for odd integers
such that
.
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References
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