ON LOCATING-DOMINATION SET OF CARTESIAN PRODUCT GRAPHS P2
A locating-domination set is defined as a set of vertices S ? V (G) such that for every two distinct vertices u, v ? V (G) \ S, ? ?= N(u) ? S ?= N(v) ? S ?= ?. The minimum cardinality of locating-domination sets of G is called the locatingdomination number of G, denoted by ?(G). The cartesian pro...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/68830 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | A locating-domination set is defined as a set of vertices S ? V (G) such that for
every two distinct vertices u, v ? V (G) \ S, ? ?= N(u) ? S ?= N(v) ? S ?= ?.
The minimum cardinality of locating-domination sets of G is called the locatingdomination
number of G, denoted by ?(G). The cartesian product graph
G?H is a graph with vertex set V (G) × V (H) and edge set E(G?H) =
{(u1, v1)(u2, v2) | u1u2 ? G, v1 = v2} ? {(u1, v1)(u2, v2) | v1v2 ? H, u1 = u2}. In
this thesis, we provide the general bounds for ?(G?P2) ? n. We also show that
those bounds are sharp. We will also determine the locating-domination number of
a cartesian product graph G?P2 for G some special graphs. |
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