$D$-MAGIC LABELING FOR ORIENTED GRAPHS
Let G be an oriented graph of order n and diameter d, and D ? {0, 1, . . . d} is set of distances in G. A D-magic labeling on an oriented graph G is a bijection f : V (G) ? {1, P 2, . . . , n} such that there exists a magic constant k that admits y?ND(x) f(y) = k for every vertex x in G, with ND(...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/71905 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let G be an oriented graph of order n and diameter d, and D ? {0, 1, . . . d} is
set of distances in G. A D-magic labeling on an oriented graph G is a bijection
f : V (G) ? {1, P 2, . . . , n} such that there exists a magic constant k that admits
y?ND(x) f(y) = k for every vertex x in G, with ND(x) = {y|d(x, y) ? D}.
In this final project, we provide a better upper bound for the magic constant k than
the previously known upper bound. We also characterize D-magic graphs with
smallest magic constant and construct D-magic graphs for most of the feasible
magic constants. Additionally, we study D-magic labelings for oriented cycles and
multipartite graphs. |
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