Graceful Labeling in the Context of Duplication of Some Graph Elements in $\bf K_{m,n}$
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Keywords:
Duplication of a vertex by an edge, duplication of an edge by a vertex, graceful labeling, $ \alpha $-labelingAbstract
In this paper, we obtained graceful labeling or $ \alpha $-labeling for some graphs obtained by duplication of some graph elements in the complete bipartite graph $K_{m,n}$.
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