LOCATING-DOMINATING SET OF HONEYCOMB NETWORK GRAPH
Architecture of microprocessor networks can be modelled with graphs. The Security of a microprocessor network architecture can be analyzed by using locating-dominating sets. A locating-dominating set is a set ÿ ? ý(ÿ) where for every vertices ÿ, ? ? ý(ÿ) ? ÿ, the neighborhood of vertex ÿ that are...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/71805 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Architecture of microprocessor networks can be modelled with graphs. The Security of
a microprocessor network architecture can be analyzed by using locating-dominating
sets. A locating-dominating set is a set ÿ ? ý(ÿ) where for every vertices ÿ, ? ? ý(ÿ) ?
ÿ, the neighborhood of vertex ÿ that are members of set S is different from the
neighborhood of vertex ? that are members of set S. The minimal cardinality of the set S
for a graph ÿ is called the location-domination number of graph G, denoted by ??(ÿ). A
honeycomb network graph or ?ÿ(??) is a graph that is formed from the recursion of
hexagonal tesselation patterns. In this research, the location-domination number of a
?ÿ(??) graph is determined. In particular, it is proved that ??(?ÿ(??)) is 3,9, and 18
where ?? is 1,2, and 3 respectively. It is also shown that the location-domination number
of a ?ÿ(??) graph with ??g 4 does not exceed ??(?ÿ(??2 3)) + 6 + 6(??2 1) +
6(??2 2). |
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