Algorithm for Determining Locating-chromatic Number of Trees
The concept of the locating-chromatic number for graphs was introduced by Chartrand et al (2002). Determination of the locating-chromatic number of an arbitrary graph is an NP-complete Problem. This means that there is no efficient algorithm to determine the locating-chromatic number of any given...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/38771 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | The concept of the locating-chromatic number for graphs was introduced by
Chartrand et al (2002). Determination of the locating-chromatic number of
an arbitrary graph is an NP-complete Problem. This means that there is no
efficient algorithm to determine the locating-chromatic number of any given graph.
However, we can arrange a special algorithm to determine the locating-chromatic
number of a certain class of graphs.
In this paper, we focus on an algorithm to determine the upper bound of the
locating-chromatic number of any tree. This algorithm works better than the one
given by Furuya and Matsumoto (2019). Let T be a tree. A vertex u of T with
degree at least 3 is a local-end branch if there are at least two end-path from u. Palm
of T is local-end branch with its end-path. This algorithm is based on considering
palms on a tree. |
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