DISTANCE MAGIC LABELING ON DISTANCE-REGULAR GRAPH AND GRAPH FROM PRODUCTS GRAPH
LetGbe a graph with order n and diameter d. LetD f0; 1; 2; :::; dg andND(v) = fu 2 V (G)jd(u; v) 2 Dg, where v 2 V (G). A bijection l : V (G) ????! f1; 2; :::; ng is calledD-distance P magic labeling of G if there is a nonnegative integer k such that u2ND(v) l(u) = k for every v 2 V (G). If D =...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/36300 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | LetGbe a graph with order n and diameter d. LetD f0; 1; 2; :::; dg andND(v) =
fu 2 V (G)jd(u; v) 2 Dg, where v 2 V (G). A bijection l : V (G) ????! f1; 2; :::; ng
is calledD-distance P magic labeling of G if there is a nonnegative integer k such that
u2ND(v) l(u) = k for every v 2 V (G). If D = f1g, D-distance magic labeling is
called distance magic labeling.
The main objective of this thesis is the existence of distance magic labeling on
distance-regular graphs and products of graphs. Products of graphs considered
are lexicographic product and kronecker product. By using a matrix with particular
properties, distance magic labelings of some products of graph are obtained.
By considering antipodal double cover graph as a distance-regular graph, the existence
of D-distance magic labeling for the antipodal double cover graph is obtained. |
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