ON THE METRIC DIMENSION OF REGULAR AND COMPOSITION GRAPHS AND CHARACTERIZATION OF ALL GRAPHS OF ORDER N WITH METRIC DIMENSION N-3
We denote by V and E the vertex and edge set of graph G, respectively. The distance between two vertices u: v 2 V (G), denoted by dG(u: v), is the length of a shortest path from u to v in G. Let W = fw1:w2: : : : :wkg be a subset of V (G). For v 2 V (G), a representation of v with respect to W is de...
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| Format: | Dissertations |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/17319 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | We denote by V and E the vertex and edge set of graph G, respectively. The distance between two vertices u: v 2 V (G), denoted by dG(u: v), is the length of a shortest path from u to v in G. Let W = fw1:w2: : : : :wkg be a subset of V (G). For v 2 V (G), a representation of v with respect to W is defined as the k-tuple r (vjW) = (dG(v:w1): dG(v:w2): : : : : dG(v:wk)). The set W is called a resolving set of G if every two distinct vertices x, y 2 V (G) satisfy that r (xjW) 6= r (yjW). A basis of G is a resolving set of G with minimum cardinality, and the metric dimension of G refers to the cardinality of a basis and denoted by Beta (G). Finding a relation, in terms of their metric dimensions, between a graph obtained by a graph operation with the original graphs is also interesting problem. In this dissertation, we consider a graph obtained from a composition product between two graphs. The composition product of two graphs G and H, denoted by Beta (G(H) |
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