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...

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Main Author: Anggia
Format: Final Project
Language:Indonesia
Online Access:https://digilib.itb.ac.id/gdl/view/42078
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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
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