CENTROIDAL DIMENSION
Let B={w_1,w_2,…,w_k}⊆V(G) 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 non-decreasing order by their distance from x. Vertex set B is called a centroidal locating set of G if r(x)≠r(y) for every...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/26276 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let B={w_1,w_2,…,w_k}⊆V(G) 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 non-decreasing order by their distance from x. Vertex set B is called a centroidal locating set of G if r(x)≠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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