MULTISET DIMENSION OF LOBSTER GRAPH
A path-subgraph of length n, P_n (k)=(VP,EP), from a connected graph G=(V,E) is called k-central-path if for every v? V, there exists v^'? VP such that d(v,v^' )? k. A lobster graph is a tree that has a 2-central-path and two-leveled rooted-tree is a lobster graph that has a 2-central-pat...
Saved in:
| Main Author: | |
|---|---|
| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/36090 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | A path-subgraph of length n, P_n (k)=(VP,EP), from a connected graph G=(V,E) is called k-central-path if for every v? V, there exists v^'? VP such that d(v,v^' )? k. A lobster graph is a tree that has a 2-central-path and two-leveled rooted-tree is a lobster graph that has a 2-central-path of length 0.
The representation multiset of vertex v with respect to a non-empty set W? V is a multiset of distances between v and the vertices in W, denoted by r_m (v|W). If r_m (u?W)? r_m (v|W) for every pair of distinct vertices u and v of G, then W is called a resolving set of G. Moreover, if G has a resolving set, then the cardinality of a smallest resolving set is called the multiset dimension of G (denoted by md(G)). If G does not contain any resolving set, md(G)=?
In this final project, the necessary and the sufficient condition for having a finite-valued multiset dimension of two leveled rooted-trees are presented. The necessary condition for having a finite-valued multiset dimension of lobster graph is also presented
|
|---|