ON THE TOTAL RESOLVING NUMBER OF WHEELS, FANS, TREES AND JAHANGIR GRAPH
Let G be a connected graph. Let S = fs1; s2; ; skg be a subset of V (G). For any v 2 (V (G)), the coordinate of v with respect to S is f(v) = (d(v; s1); d(v; s2); ; d(v; sk)). If distinct vertices in V have distinct coordinates, then S is called a resolving set of G. The cardinality of a mi...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/44464 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let G be a connected graph. Let S = fs1; s2; ; skg be a subset of V (G). For any
v 2 (V (G)), the coordinate of v with respect to S is f(v) = (d(v; s1); d(v; s2); ; d(v; sk)).
If distinct vertices in V have distinct coordinates, then S is called a resolving set of G.
The cardinality of a minimum resolving set of G is called the metric dimension of G, (G).
A resolving set S is called a total resolving set if the induced subgraph hSi has no isolated
vertices. The cardinality of a total minimum resolving set of G is called the total resolving
number of G and it is denoted by tr(G). In this project we give a study of tr(Wn), tr(fn),
tr(Tn) and upper bound of tr(J2n), where Wn is a wheel on n + 1 vertices, fn is a fan on
n + 1 vertices, Tn is a tree on n vertices, and J2n is a Jahangir graph on 2n + 1 vertices. |
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