THE MULTISET DIMENSION OF SOME GRAPHS

• Main Author: BINTANG MULIA S (NIM: 20116022), PRESLI
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/29977
• Institution: Institut Teknologi Bandung

Let G be a connected graph, u and v be vertices in G, distance d(u,v) be the minimum length of paths connecting u and v in G. Let W={w_1,...,w_k} be an ordered set of vertices in G and v be a vertex in G, the representation of v with respect to W is the k-vector (ordered k-tuple) <br /> <br /> r(v|W)=(d(v,w_1),d(v,w_2),...,d(v,w_k)). <br /> <br /> If the representation of every vertex in G is unique, then W is a resolving set for G. A resolving set with minimum cardinality is a metric basis. <br /> <br /> <br /> If W={w_1,w_2,...,w_k} is a subset of vertices in G and v is a vertex in G, the representation multiset of v with respect to W is defined as a multiset of distances between v and the vertices in W, denoted with r_m (v|W). If r_m (v|W)&#8800;r_m (u|W) for every pair of distinct vertices u and v, then W is called a resolving set for G. A resolving set having minimum cardinality is called multiset basis. If G has a multiset basis, then it's cardinality is called multiset dimension of G, denoted md(G). <br /> <br /> <br /> In this thesis, we give multiset dimension of $k$-ary complete trees, caterpilars, Kartesian product of some graphs, circulant graphs. <br />