GRAPHS WITH MINIMUM OR MAXIMUM LOCAL METRIC DIMENSION
Let W = fw1;w2; :::;wkg be an ordered set consisting of k distinct vertices in a nontrivial connected graph G. The metric representation of a vertex v in G with respect to W is the k-vector r(vjW) = (d(v;w1); d(v;w2); :::; d(v;wk)) where d(v;wi) represents the distance between v and wi for some...
Saved in:
Main Author: | |
---|---|
Format: | Final Project |
Language: | Indonesia |
Online Access: | https://digilib.itb.ac.id/gdl/view/42078 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Institution: | Institut Teknologi Bandung |
Language: | Indonesia |
id |
id-itb.:42078 |
---|---|
spelling |
id-itb.:420782019-09-13T09:51:10ZGRAPHS WITH MINIMUM OR MAXIMUM LOCAL METRIC DIMENSION Anggia Indonesia Final Project local metric representation, local resolving set, local metric dimension, local metric basis. INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/42078 Let W = fw1;w2; :::;wkg be an ordered set consisting of k distinct vertices in a nontrivial connected graph G. The metric representation of a vertex v in G with respect to W is the k-vector r(vjW) = (d(v;w1); d(v;w2); :::; d(v;wk)) where d(v;wi) represents the distance between v and wi for some 1 i k. If for any arbitrary pair of adjacent vertices u and v in G satisfies r(ujW) 6= r(vjW), then W is a local metric set of G. The smallest positive integer k such that G has a local metric k-set is called the local metric dimension of G (lmd(G)). A local metric set of G having cardinality lmd(G) is a local metric basis of G. Moreover, let n be the order of G, l be the number of true twin equivalence classes in G, and d be the diameter of G. Then, G satisfies lmd(G) n????l and lmd(G) n ???? d: In this final project, some nontrivial connected graphs G with lmd(G) = n ???? l or lmd(G) = n ???? d will be presented. text |
institution |
Institut Teknologi Bandung |
building |
Institut Teknologi Bandung Library |
continent |
Asia |
country |
Indonesia Indonesia |
content_provider |
Institut Teknologi Bandung |
collection |
Digital ITB |
language |
Indonesia |
description |
Let W = fw1;w2; :::;wkg be an ordered set consisting of k distinct vertices in a
nontrivial connected graph G. The metric representation of a vertex v in G with
respect to W is the k-vector
r(vjW) = (d(v;w1); d(v;w2); :::; d(v;wk))
where d(v;wi) represents the distance between v and wi for some 1 i k. If for
any arbitrary pair of adjacent vertices u and v in G satisfies r(ujW) 6= r(vjW), then
W is a local metric set of G. The smallest positive integer k such that G has a local
metric k-set is called the local metric dimension of G (lmd(G)). A local metric set
of G having cardinality lmd(G) is a local metric basis of G.
Moreover, let n be the order of G, l be the number of true twin equivalence classes
in G, and d be the diameter of G. Then, G satisfies lmd(G) n????l and lmd(G)
n ???? d:
In this final project, some nontrivial connected graphs G with lmd(G) = n ???? l or
lmd(G) = n ???? d will be presented. |
format |
Final Project |
author |
Anggia |
spellingShingle |
Anggia GRAPHS WITH MINIMUM OR MAXIMUM LOCAL METRIC DIMENSION |
author_facet |
Anggia |
author_sort |
Anggia |
title |
GRAPHS WITH MINIMUM OR MAXIMUM LOCAL METRIC DIMENSION |
title_short |
GRAPHS WITH MINIMUM OR MAXIMUM LOCAL METRIC DIMENSION |
title_full |
GRAPHS WITH MINIMUM OR MAXIMUM LOCAL METRIC DIMENSION |
title_fullStr |
GRAPHS WITH MINIMUM OR MAXIMUM LOCAL METRIC DIMENSION |
title_full_unstemmed |
GRAPHS WITH MINIMUM OR MAXIMUM LOCAL METRIC DIMENSION |
title_sort |
graphs with minimum or maximum local metric dimension |
url |
https://digilib.itb.ac.id/gdl/view/42078 |
_version_ |
1821998508974014464 |