METRIC DIMENSION OF COMPLETE BIPARTITE DIGRAPHS
Let D be a digraph and n is the order of D: Let W = fw1;w2; :::;wkg be an ordered subset of V (D) and v be a vertex of D: A representation of v with respect to W is a k-vector r(vjW) = (d(v;w1); d(v;w2); :::; d(v;wk)), where d(x; y) denotes the directed distance of x to y; that is the length of t...
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| Format: | Theses |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/33943 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let D be a digraph and n is the order of D: Let W = fw1;w2; :::;wkg be an ordered subset
of V (D) and v be a vertex of D: A representation of v with respect to W is a k-vector
r(vjW) = (d(v;w1); d(v;w2); :::; d(v;wk)), where d(x; y) denotes the directed distance of x
to y; that is the length of the shortest directed path from x to y in D: If all vertices have
representations and if two distinct vertices of D have distinct representation then W is a
resolving set of D: The minimum cardinality of resolving set in D is the directed dimension
or the metric dimension dim(D) of D: In this thesis we provide a sucient conditions for
2-dimensional digraph and discuss metric dimension of complete bipartite digraphs. |
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