CENTROIDAL DIMENSION
Let B = (Rumus) be a set of vertices, and x be any vertex in G. We denote r(x) as an ordered partition of B, that is a list of subsets of B in nondecreasing order by their distance from x. Vertex set B is called a centroidal locating set of G if r(x) 6= r(y) for every pair x;y of distinct vertice...
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| Format: | Theses |
| Language: | Indonesia |
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| Online Access: | https://digilib.itb.ac.id/gdl/view/32467 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let B = (Rumus) be a set of vertices, and x be any vertex in G.
We denote r(x) as an ordered partition of B, that is a list of subsets of B in nondecreasing
order by their distance from x. Vertex set B is called a centroidal locating
set of G if r(x) 6= r(y) for every pair x;y of distinct vertices. A centroidal basis of
G is a centroidal locating set of minimum cardinality. The centroidal dimension
of G, denoted by CD(G), is the cardinality of centroidal basis of G. In this thesis,
we give results about the centroidal dimension of some families of graphs and the
centroidal dimension of circulant graph. We also study the centroidal dimension of
join and corona of two graphs. In particular, we give results about the centroidal
dimension of tensor product and cartesius product of complete graph and path with
order 2. We also study the algorithm to determine the centroidal dimension of graph
by its adjacency matrix. |
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