The local metric dimension of subgraph-amalgamation of graphs

A vertex $v$ is said to distinguish two other vertices $x$ and $y$ of a nontrivial connected graph G if the distance from $v$ to $x$ is different from the distance from $v$ to $y$. A set $S\subseteq V(G)$ is a local metric set for $G$ if every two adjacent vertices of $G$ are distinguished by some v...

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Bibliographic Details
Main Authors Barragan-Ramirez, Gabriel A, Simanjuntak, Rinovia, Saputro, Suhadi W, Uttunggadewa, Saladin
Format Journal Article
LanguageEnglish
Published 23.12.2015
Subjects
Mathematics - Combinatorics
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Summary:A vertex $v$ is said to distinguish two other vertices $x$ and $y$ of a nontrivial connected graph G if the distance from $v$ to $x$ is different from the distance from $v$ to $y$. A set $S\subseteq V(G)$ is a local metric set for $G$ if every two adjacent vertices of $G$ are distinguished by some vertex of $S$. A local metric set with minimum cardinality is called a local metric basis for $G$ and its cardinality, the local metric dimension of $G$, denoted by $\dim_l(G)$. In this paper we present tight bounds for the local metric dimension of subgraph-amalgamation of graphs with special emphasis in the case of subgraphs which are isometric embeddings.
DOI:10.48550/arxiv.1512.07420