THE LOCAL METRIC DIMENSION OF CIRCULANTGRAPHS

• Main Author: Alif Darmamulia, Muhammad
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/72827
• Institution: Institut Teknologi Bandung

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)