THE LOCAL METRIC DIMENSION OF MYCIELSKI'S GRAPH
An ordered set W is called local metric set of G if every two adjacent vertices in G have different representation to W. The minimum cardinality of local metric set of G is called local metric dimension of G, denoted by lmd(G). For a connected graph G with vertex set V(G)={v_1, v_2,…,v_n} and ed...
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id-itb.:235692017-09-27T14:41:49ZTHE LOCAL METRIC DIMENSION OF MYCIELSKI'S GRAPH FAHRI TADJUDDIN (90115012), NUR Indonesia Theses INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/23569 An ordered set W is called local metric set of G if every two adjacent vertices in G have different representation to W. The minimum cardinality of local metric set of G is called local metric dimension of G, denoted by lmd(G). For a connected graph G with vertex set V(G)={v_1, v_2,…,v_n} and edge set E(G), the Mycielski's graph of G, denoted by μ(G), is graph with vertex set V(μ(G))={x_1,…,x_n,y_1,…,y_n,z} and edge set {x_i x_j| v_i v_j∈E(G)}∪{x_i y_j| v_i v_j∈E(G)}∪{y_i z| 1≤i≤n}. In this project, we determine the bounds of local metric dimension of Mycielski's graph of connected graph G. text |
| institution |
Institut Teknologi Bandung |
| building |
Institut Teknologi Bandung Library |
| continent |
Asia |
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Indonesia Indonesia |
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Institut Teknologi Bandung |
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Digital ITB |
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Indonesia |
| description |
An ordered set W is called local metric set of G if every two adjacent vertices in G have different representation to W. The minimum cardinality of local metric set of G is called local metric dimension of G, denoted by lmd(G). For a connected graph G with vertex set V(G)={v_1, v_2,…,v_n} and edge set E(G), the Mycielski's graph of G, denoted by μ(G), is graph with vertex set V(μ(G))={x_1,…,x_n,y_1,…,y_n,z} and edge set {x_i x_j| v_i v_j∈E(G)}∪{x_i y_j| v_i v_j∈E(G)}∪{y_i z| 1≤i≤n}. In this project, we determine the bounds of local metric dimension of Mycielski's graph of connected graph G. |
| format |
Theses |
| author |
FAHRI TADJUDDIN (90115012), NUR |
| spellingShingle |
FAHRI TADJUDDIN (90115012), NUR THE LOCAL METRIC DIMENSION OF MYCIELSKI'S GRAPH |
| author_facet |
FAHRI TADJUDDIN (90115012), NUR |
| author_sort |
FAHRI TADJUDDIN (90115012), NUR |
| title |
THE LOCAL METRIC DIMENSION OF MYCIELSKI'S GRAPH |
| title_short |
THE LOCAL METRIC DIMENSION OF MYCIELSKI'S GRAPH |
| title_full |
THE LOCAL METRIC DIMENSION OF MYCIELSKI'S GRAPH |
| title_fullStr |
THE LOCAL METRIC DIMENSION OF MYCIELSKI'S GRAPH |
| title_full_unstemmed |
THE LOCAL METRIC DIMENSION OF MYCIELSKI'S GRAPH |
| title_sort |
local metric dimension of mycielski's graph |
| url |
https://digilib.itb.ac.id/gdl/view/23569 |
| _version_ |
1823634643833847808 |