THE LOCAL METRIC DIMENSION OF CIRCULANTGRAPHS
For an ordered set W = {w1,w2, ...,wk} of k distinct vertices of a connected graph G, the metric representation of a vertex v ? V (G) with respect toW is the k-vector r(v|W) = (d(v,w1), d(v,w2), ..., d(v,wk)), where d(v,wi) is the distance between v and wi for 1 ? i ? k. The set W is a resolving...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/72827 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | For an ordered set W = {w1,w2, ...,wk} of k distinct vertices of a connected graph
G, the metric representation of a vertex v ? V (G) with respect toW is the k-vector
r(v|W) = (d(v,w1), d(v,w2), ..., d(v,wk)), where d(v,wi) is the distance between
v and wi for 1 ? i ? k. The set W is a resolving set for G if r(u|W) = r(v|W)
implies that u = v for all pairs u, v ? V (G). The minimum cardinality of a
resolving set for G is metric dimension of G. If for every of adjacent vertices
u?, v? ? V (G), r(u?|W) ?= r(v?|W), then W is a local resolving set and the
minimum cardinality of the set is the local metric dimension of G.
A circulant graph with parameter a1, a2, ..., ak, denoted by Cn(a1, a2, ..., ak), is
an n-vertex connected graph where each vertex vi is adjacent to the vertices
v(i+aj ) (mod n) for j = 1, ..., k.
This research studies the local metric dimension of the circulant graphs Cn(1, k) for
k = 3, 4, 5, n ? 6 and Cn(1, n?1
2 ) for n ? 1 (mod 4) |
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