THE LOCATING-CHROMATIC NUMBER OF D(r;k) TREE
Let G be a simple connected graph and c a proper coloring of G. A color code of a vertex v is an ordered k-tuple cP(v) = (d(v;C1);d(v;C2);d(v;C3); .....d(v;Ci)) where P is a partition of vertex set in G constructed by a proper coloring c, and d(v;Ci) is the distance of v to Ci. A locating colorin...
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| Format: | Final Project |
| Language: | Indonesia |
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| Online Access: | https://digilib.itb.ac.id/gdl/view/34134 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let G be a simple connected graph and c a proper coloring of G. A color code
of a vertex v is an ordered k-tuple cP(v) = (d(v;C1);d(v;C2);d(v;C3); .....d(v;Ci))
where P is a partition of vertex set in G constructed by a proper coloring c, and
d(v;Ci) is the distance of v to Ci. A locating coloring of is a proper coloring where
all vertices have distinct color codes. The minimum number of colors such that G
has a locating coloring is called the locating-chromatic number, denoted by cL(G).
The locating-chromatic number was first studied by Chatrand et al. in 2002. In
this final project we determine the locating-chromatic number of D(r;k) for some
r. D(r;k) is a tree which has diameter r and all vertices except leaves have degree
k.
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